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Properties

Label 25215.h
Number of curves $2$
Conductor $25215$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 25215.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25215.h1 25215c1 \([1, 1, 0, -5262, -146889]\) \(233858751281/4100625\) \(282619175625\) \([2]\) \(40960\) \(0.99376\) \(\Gamma_0(N)\)-optimal
25215.h2 25215c2 \([1, 1, 0, -137, -414414]\) \(-4173281/1076168025\) \(-74170576451025\) \([2]\) \(81920\) \(1.3403\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25215.h have rank \(0\).

Complex multiplication

The elliptic curves in class 25215.h do not have complex multiplication.

Modular form 25215.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.