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Properties

Label 25350.dc
Number of curves $2$
Conductor $25350$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 25350.dc have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 25350.dc do not have complex multiplication.

Modular form 25350.2.a.dc

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 6 q^{11} + q^{12} + q^{16} - 6 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 25350.dc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.dc1 25350dc1 \([1, 0, 0, -94897813, -342713012383]\) \(570403428460237/23887872000\) \(3958108181973504000000000\) \([2]\) \(8087040\) \(3.4846\) \(\Gamma_0(N)\)-optimal
25350.dc2 25350dc2 \([1, 0, 0, 45710187, -1271428852383]\) \(63745936931123/4251528000000\) \(-704458218910811625000000000\) \([2]\) \(16174080\) \(3.8312\)