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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 123840eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.gg2 | 123840eb1 | \([0, 0, 0, -492, -176]\) | \(1860867/1075\) | \(7608729600\) | \([2]\) | \(65536\) | \(0.58555\) | \(\Gamma_0(N)\)-optimal |
| 123840.gg1 | 123840eb2 | \([0, 0, 0, -5292, 147664]\) | \(2315685267/9245\) | \(65435074560\) | \([2]\) | \(131072\) | \(0.93213\) |
Rank
sage: E.rank()
The elliptic curves in class 123840eb have rank \(1\).
Complex multiplication
The elliptic curves in class 123840eb do not have complex multiplication.Modular form 123840.2.a.eb
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.
