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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 76050ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.bd2 | 76050ci1 | \([1, -1, 0, -23607, 1219401]\) | \(3307949/468\) | \(205846510018500\) | \([2]\) | \(344064\) | \(1.4725\) | \(\Gamma_0(N)\)-optimal |
| 76050.bd1 | 76050ci2 | \([1, -1, 0, -99657, -10872549]\) | \(248858189/27378\) | \(12042020836082250\) | \([2]\) | \(688128\) | \(1.8190\) |
Rank
sage: E.rank()
The elliptic curves in class 76050ci have rank \(1\).
Complex multiplication
The elliptic curves in class 76050ci do not have complex multiplication.Modular form 76050.2.a.ci
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.
