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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 457776.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.m1 | 457776m1 | \([0, 0, 0, -76878624, 259541841584]\) | \(-2412468600832/970299\) | \(-20210843124037641056256\) | \([]\) | \(59222016\) | \(3.2435\) | \(\Gamma_0(N)\)-optimal |
| 457776.m2 | 457776m2 | \([0, 0, 0, 50466336, 1002090303344]\) | \(682417553408/21221529219\) | \(-442033845131645029966196736\) | \([]\) | \(177666048\) | \(3.7928\) |
Rank
sage: E.rank()
The elliptic curves in class 457776.m have rank \(0\).
Complex multiplication
The elliptic curves in class 457776.m do not have complex multiplication.Modular form 457776.2.a.m
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.
