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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 19320.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19320.f1 | 19320p1 | \([0, -1, 0, -188056, 22811356]\) | \(718269868008155236/197344270832625\) | \(202080533332608000\) | \([2]\) | \(211200\) | \(2.0282\) | \(\Gamma_0(N)\)-optimal |
| 19320.f2 | 19320p2 | \([0, -1, 0, 484224, 148393260]\) | \(6131006771007815422/8203108300734375\) | \(-16799965799904000000\) | \([2]\) | \(422400\) | \(2.3748\) |
Rank
sage: E.rank()
The elliptic curves in class 19320.f have rank \(0\).
Complex multiplication
The elliptic curves in class 19320.f do not have complex multiplication.Modular form 19320.2.a.f
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 LMFDB 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 LMFDB labels.
