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Properties

Label 25270.l
Number of curves $2$
Conductor $25270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 25270.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25270.l1 25270l1 \([1, 1, 0, -590242, -182923404]\) \(-483385461758641/26693632000\) \(-1255825434529792000\) \([]\) \(777600\) \(2.2307\) \(\Gamma_0(N)\)-optimal
25270.l2 25270l2 \([1, 1, 0, 3164158, -358687084]\) \(74469146542554959/44285662466080\) \(-2083458006385366216480\) \([]\) \(2332800\) \(2.7800\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25270.l have rank \(0\).

Complex multiplication

The elliptic curves in class 25270.l do not have complex multiplication.

Modular form 25270.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} + q^{5} - 2 q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - 3 q^{11} + 2 q^{12} + 7 q^{13} - q^{14} + 2 q^{15} + q^{16} + 3 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.