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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 33813j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33813.f1 | 33813j1 | \([1, -1, 0, -1685349, 842484024]\) | \(147815204204011553/15178486401\) | \(54362917788634377\) | \([2]\) | \(638976\) | \(2.2441\) | \(\Gamma_0(N)\)-optimal |
| 33813.f2 | 33813j2 | \([1, -1, 0, -1556064, 977069709]\) | \(-116340772335201233/47730591665289\) | \(-170950789304790780753\) | \([2]\) | \(1277952\) | \(2.5907\) |
Rank
sage: E.rank()
The elliptic curves in class 33813j have rank \(0\).
Complex multiplication
The elliptic curves in class 33813j do not have complex multiplication.Modular form 33813.2.a.j
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.
