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Properties

Label 369600.tc
Number of curves $4$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("tc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 369600.tc have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 369600.tc do not have complex multiplication.

Modular form 369600.2.a.tc

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 369600.tc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.tc1 369600tc3 \([0, 1, 0, -1629469633, 22422540588863]\) \(233632133015204766393938/29145526885986328125\) \(59690039062500000000000000000\) \([2]\) \(377487360\) \(4.2512\)  
369600.tc2 369600tc2 \([0, 1, 0, -407017633, -2797866623137]\) \(7282213870869695463556/912102595400390625\) \(933993057690000000000000000\) \([2, 2]\) \(188743680\) \(3.9047\)  
369600.tc3 369600tc1 \([0, 1, 0, -393895633, -3009065213137]\) \(26401417552259125806544/507547744790625\) \(129932222666400000000000\) \([2]\) \(94371840\) \(3.5581\) \(\Gamma_0(N)\)-optimal
369600.tc4 369600tc4 \([0, 1, 0, 605482367, -14501354123137]\) \(11986661998777424518222/51295853620928503125\) \(-105053908215661574400000000000\) \([2]\) \(377487360\) \(4.2512\)