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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 31790h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31790.b1 | 31790h1 | \([1, 1, 0, -25582, 1579316]\) | \(-76711450249/851840\) | \(-20561346776960\) | \([]\) | \(141120\) | \(1.3694\) | \(\Gamma_0(N)\)-optimal |
31790.b2 | 31790h2 | \([1, 1, 0, 85683, 8277469]\) | \(2882081488391/2883584000\) | \(-69602707767296000\) | \([]\) | \(423360\) | \(1.9187\) |
Rank
sage: E.rank()
The elliptic curves in class 31790h have rank \(0\).
Complex multiplication
The elliptic curves in class 31790h do not have complex multiplication.Modular form 31790.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.