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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 141120.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.cr1 | 141120ng1 | \([0, 0, 0, -3716748, -2757999888]\) | \(-5154200289/20\) | \(-22033412542955520\) | \([]\) | \(2257920\) | \(2.3492\) | \(\Gamma_0(N)\)-optimal |
| 141120.cr2 | 141120ng2 | \([0, 0, 0, 25918452, 26168326128]\) | \(1747829720511/1280000000\) | \(-1410138402749153280000000\) | \([]\) | \(15805440\) | \(3.3221\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.cr do not have complex multiplication.Modular form 141120.2.a.cr
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
