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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 350658u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.u1 | 350658u1 | \([1, -1, 0, -9148167, 10652299389]\) | \(-65560514292015625/149954112\) | \(-193660932467838528\) | \([]\) | \(14100480\) | \(2.5609\) | \(\Gamma_0(N)\)-optimal |
| 350658.u2 | 350658u2 | \([1, -1, 0, -6289542, 17419213620]\) | \(-21305767155765625/89149883547648\) | \(-115134219041867477286912\) | \([]\) | \(42301440\) | \(3.1102\) |
Rank
sage: E.rank()
The elliptic curves in class 350658u have rank \(2\).
Complex multiplication
The elliptic curves in class 350658u do not have complex multiplication.Modular form 350658.2.a.u
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.
