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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)
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.