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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 56277c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56277.j3 | 56277c1 | \([0, 0, 1, -5070, -137862]\) | \(4096000/37\) | \(130193519157\) | \([]\) | \(43200\) | \(0.95525\) | \(\Gamma_0(N)\)-optimal |
| 56277.j2 | 56277c2 | \([0, 0, 1, -35490, 2491947]\) | \(1404928000/50653\) | \(178234927725933\) | \([]\) | \(129600\) | \(1.5046\) | |
| 56277.j1 | 56277c3 | \([0, 0, 1, -2849340, 1851247674]\) | \(727057727488000/37\) | \(130193519157\) | \([]\) | \(388800\) | \(2.0539\) |
Rank
sage: E.rank()
The elliptic curves in class 56277c have rank \(0\).
Complex multiplication
The elliptic curves in class 56277c do not have complex multiplication.Modular form 56277.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
