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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 39270c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39270.c2 | 39270c1 | \([1, 1, 0, -708428, 228706128]\) | \(39319847421423003352009/99770836591641600\) | \(99770836591641600\) | \([2]\) | \(675840\) | \(2.1385\) | \(\Gamma_0(N)\)-optimal |
39270.c1 | 39270c2 | \([1, 1, 0, -982828, 34815088]\) | \(104992182751869695281609/60223351327875600480\) | \(60223351327875600480\) | \([2]\) | \(1351680\) | \(2.4851\) |
Rank
sage: E.rank()
The elliptic curves in class 39270c have rank \(1\).
Complex multiplication
The elliptic curves in class 39270c do not have complex multiplication.Modular form 39270.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.