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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1210j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1210.k1 | 1210j1 | \([1, 0, 0, -10711, -431639]\) | \(-76711450249/851840\) | \(-1509086522240\) | \([]\) | \(3360\) | \(1.1518\) | \(\Gamma_0(N)\)-optimal |
1210.k2 | 1210j2 | \([1, 0, 0, 35874, -2229820]\) | \(2882081488391/2883584000\) | \(-5108444954624000\) | \([]\) | \(10080\) | \(1.7011\) |
Rank
sage: E.rank()
The elliptic curves in class 1210j have rank \(1\).
Complex multiplication
The elliptic curves in class 1210j do not have complex multiplication.Modular form 1210.2.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 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.