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Properties

Label 248430t
Number of curves $8$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("t1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 248430t have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 248430t do not have complex multiplication.

Modular form 248430.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} + q^{15} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 248430t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248430.t7 248430t1 \([1, 1, 0, -339693, 26672157]\) \(7633736209/3870720\) \(2198062871260139520\) \([2]\) \(5308416\) \(2.2120\) \(\Gamma_0(N)\)-optimal
248430.t5 248430t2 \([1, 1, 0, -2989613, -1971897507]\) \(5203798902289/57153600\) \(32455772083450497600\) \([2, 2]\) \(10616832\) \(2.5586\)  
248430.t4 248430t3 \([1, 1, 0, -22201533, 40255240173]\) \(2131200347946769/2058000\) \(1168674920700378000\) \([2]\) \(15925248\) \(2.7613\)  
248430.t6 248430t4 \([1, 1, 0, -670933, -4949546363]\) \(-58818484369/18600435000\) \(-10562615111087237835000\) \([2]\) \(21233664\) \(2.9052\)  
248430.t2 248430t5 \([1, 1, 0, -47707013, -126849708747]\) \(21145699168383889/2593080\) \(1472530400082476280\) \([2]\) \(21233664\) \(2.9052\)  
248430.t3 248430t6 \([1, 1, 0, -22367153, 39623929857]\) \(2179252305146449/66177562500\) \(37580202918771530062500\) \([2, 2]\) \(31850496\) \(3.1079\)  
248430.t8 248430t7 \([1, 1, 0, 6036677, 133419057283]\) \(42841933504271/13565917968750\) \(-7703667690163624511718750\) \([2]\) \(63700992\) \(3.4545\)  
248430.t1 248430t8 \([1, 1, 0, -53420903, -94571745393]\) \(29689921233686449/10380965400750\) \(5895031057587402320430750\) \([2]\) \(63700992\) \(3.4545\)