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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 980.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 980.e1 | 980f1 | \([0, -1, 0, -48820, -4138168]\) | \(-177953104/125\) | \(-9039207968000\) | \([]\) | \(3024\) | \(1.4223\) | \(\Gamma_0(N)\)-optimal |
| 980.e2 | 980f2 | \([0, -1, 0, 47220, -17660600]\) | \(161017136/1953125\) | \(-141237624500000000\) | \([]\) | \(9072\) | \(1.9716\) |
Rank
sage: E.rank()
The elliptic curves in class 980.e have rank \(0\).
Complex multiplication
The elliptic curves in class 980.e do not have complex multiplication.Modular form 980.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
