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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 450528i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450528.i1 | 450528i1 | \([0, -1, 0, -5174, -113100]\) | \(5088448/1053\) | \(3170516012352\) | \([2]\) | \(838656\) | \(1.1139\) | \(\Gamma_0(N)\)-optimal |
| 450528.i2 | 450528i2 | \([0, -1, 0, 11071, -694671]\) | \(778688/1521\) | \(-293096591364096\) | \([2]\) | \(1677312\) | \(1.4605\) |
Rank
sage: E.rank()
The elliptic curves in class 450528i have rank \(1\).
Complex multiplication
The elliptic curves in class 450528i do not have complex multiplication.Modular form 450528.2.a.i
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.
