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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 355740cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.cg2 | 355740cg1 | \([0, -1, 0, -58725, -4536783]\) | \(1007878144/179685\) | \(3993042937847040\) | \([]\) | \(1866240\) | \(1.7129\) | \(\Gamma_0(N)\)-optimal |
| 355740.cg1 | 355740cg2 | \([0, -1, 0, -4530885, -3710615775]\) | \(462893166690304/4125\) | \(91667652384000\) | \([]\) | \(5598720\) | \(2.2622\) |
Rank
sage: E.rank()
The elliptic curves in class 355740cg have rank \(1\).
Complex multiplication
The elliptic curves in class 355740cg do not have complex multiplication.Modular form 355740.2.a.cg
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.
