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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 201019e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201019.e2 | 201019e1 | \([0, 1, 1, -16199, -800415]\) | \(-43614208/91\) | \(-980908594939\) | \([]\) | \(422280\) | \(1.1866\) | \(\Gamma_0(N)\)-optimal |
| 201019.e3 | 201019e2 | \([0, 1, 1, 27981, -3934986]\) | \(224755712/753571\) | \(-8122904074689859\) | \([]\) | \(1266840\) | \(1.7359\) | |
| 201019.e1 | 201019e3 | \([0, 1, 1, -259189, 125090495]\) | \(-178643795968/524596891\) | \(-5654742849012942139\) | \([]\) | \(3800520\) | \(2.2852\) |
Rank
sage: E.rank()
The elliptic curves in class 201019e have rank \(1\).
Complex multiplication
The elliptic curves in class 201019e do not have complex multiplication.Modular form 201019.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
