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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 40425.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40425.h1 | 40425bi2 | \([1, 1, 1, -2070888, -263657094]\) | \(4274401176989/2343775203\) | \(538560173550287109375\) | \([2]\) | \(1382400\) | \(2.6686\) | |
40425.h2 | 40425bi1 | \([1, 1, 1, -1244013, 530142906]\) | \(926574216749/6792093\) | \(1560708885462890625\) | \([2]\) | \(691200\) | \(2.3221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40425.h have rank \(1\).
Complex multiplication
The elliptic curves in class 40425.h do not have complex multiplication.Modular form 40425.2.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 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.