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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 19350e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19350.bc2 | 19350e1 | \([1, -1, 0, -16917, -813259]\) | \(1740992427/68800\) | \(21159225000000\) | \([2]\) | \(55296\) | \(1.3238\) | \(\Gamma_0(N)\)-optimal |
| 19350.bc1 | 19350e2 | \([1, -1, 0, -43917, 2453741]\) | \(30459021867/9245000\) | \(2843270859375000\) | \([2]\) | \(110592\) | \(1.6703\) |
Rank
sage: E.rank()
The elliptic curves in class 19350e have rank \(0\).
Complex multiplication
The elliptic curves in class 19350e do not have complex multiplication.Modular form 19350.2.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.
