Properties

Label 9025h
Number of curves $2$
Conductor $9025$
CM no
Rank $1$
Graph

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

Elliptic curves in class 9025h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.c2 9025h1 \([1, -1, 1, 2820, -2010178]\) \(27/19\) \(-1745843240234375\) \([2]\) \(28800\) \(1.6037\) \(\Gamma_0(N)\)-optimal
9025.c1 9025h2 \([1, -1, 1, -222805, -39463928]\) \(13312053/361\) \(33171021564453125\) \([2]\) \(57600\) \(1.9503\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9025h have rank \(1\).

Complex multiplication

The elliptic curves in class 9025h do not have complex multiplication.

Modular form 9025.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 2 q^{7} + 3 q^{8} - 3 q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{14} - q^{16} - 4 q^{17} + 3 q^{18} + O(q^{20})\) 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 Cremona 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 Cremona labels.