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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 277200e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.e2 | 277200e1 | \([0, 0, 0, -6031875, 1092667509250]\) | \(-520203426765625/11054534935707648\) | \(-515760381960376025088000000\) | \([2]\) | \(115015680\) | \(3.8045\) | \(\Gamma_0(N)\)-optimal |
| 277200.e1 | 277200e2 | \([0, 0, 0, -1628047875, 24924948597250]\) | \(10228636028672744397625/167006381634183168\) | \(7791849741524449886208000000\) | \([2]\) | \(230031360\) | \(4.1511\) |
Rank
sage: E.rank()
The elliptic curves in class 277200e have rank \(1\).
Complex multiplication
The elliptic curves in class 277200e do not have complex multiplication.Modular form 277200.2.a.e
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.
