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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 19650m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19650.r1 | 19650m1 | \([1, 0, 1, -1776, -28802]\) | \(39616946929/226368\) | \(3537000000\) | \([2]\) | \(23040\) | \(0.67369\) | \(\Gamma_0(N)\)-optimal |
19650.r2 | 19650m2 | \([1, 0, 1, -776, -60802]\) | \(-3301293169/100082952\) | \(-1563796125000\) | \([2]\) | \(46080\) | \(1.0203\) |
Rank
sage: E.rank()
The elliptic curves in class 19650m have rank \(0\).
Complex multiplication
The elliptic curves in class 19650m do not have complex multiplication.Modular form 19650.2.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 Cremona 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 Cremona labels.