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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 363726.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363726.j1 | 363726j2 | \([1, -1, 0, -135603, -19133955]\) | \(213525509833/669336\) | \(864426004498584\) | \([2]\) | \(2949120\) | \(1.7334\) | |
363726.j2 | 363726j1 | \([1, -1, 0, -4923, -551259]\) | \(-10218313/96192\) | \(-124228886874048\) | \([2]\) | \(1474560\) | \(1.3868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363726.j have rank \(0\).
Complex multiplication
The elliptic curves in class 363726.j do not have complex multiplication.Modular form 363726.2.a.j
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.