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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 350064ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.ba2 | 350064ba1 | \([0, 0, 0, -20355, 783234]\) | \(8433606238875/2484248624\) | \(274738023825408\) | \([2]\) | \(933888\) | \(1.4764\) | \(\Gamma_0(N)\)-optimal |
| 350064.ba1 | 350064ba2 | \([0, 0, 0, -297795, 62541378]\) | \(26409015101734875/3994998436\) | \(441814867034112\) | \([2]\) | \(1867776\) | \(1.8229\) |
Rank
sage: E.rank()
The elliptic curves in class 350064ba have rank \(1\).
Complex multiplication
The elliptic curves in class 350064ba do not have complex multiplication.Modular form 350064.2.a.ba
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.
