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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 363726.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363726.v1 | 363726v2 | \([1, -1, 0, -3668396892, 4954527083600]\) | \(156568813065172464046875/90302947539489980416\) | \(3148830834845544152199934967808\) | \([2]\) | \(468910080\) | \(4.5416\) | |
363726.v2 | 363726v1 | \([1, -1, 0, -2597866332, 50839393840208]\) | \(55606647632008753582875/159430298424049664\) | \(5559276339974825648672735232\) | \([2]\) | \(234455040\) | \(4.1950\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363726.v have rank \(1\).
Complex multiplication
The elliptic curves in class 363726.v do not have complex multiplication.Modular form 363726.2.a.v
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.