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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 6762.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6762.m1 | 6762t2 | \([1, 0, 1, -12262962, -16528997180]\) | \(1733490909744055732873/99355964553216\) | \(11689129873721309184\) | \([2]\) | \(405504\) | \(2.7224\) | |
6762.m2 | 6762t1 | \([1, 0, 1, -722482, -289233724]\) | \(-354499561600764553/101902222098432\) | \(-11988694527658426368\) | \([2]\) | \(202752\) | \(2.3759\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6762.m have rank \(0\).
Complex multiplication
The elliptic curves in class 6762.m do not have complex multiplication.Modular form 6762.2.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.