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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 236992.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.m1 | 236992m2 | \([0, 1, 0, -20500513, -33454460865]\) | \(24553362849625/1755162752\) | \(68112109622265519276032\) | \([2]\) | \(22708224\) | \(3.1282\) | |
| 236992.m2 | 236992m1 | \([0, 1, 0, 1167327, -2283106241]\) | \(4533086375/60669952\) | \(-2354401844896026591232\) | \([2]\) | \(11354112\) | \(2.7816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.m have rank \(2\).
Complex multiplication
The elliptic curves in class 236992.m do not have complex multiplication.Modular form 236992.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
