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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 37191.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37191.a1 | 37191a2 | \([1, 1, 1, -9339, -351114]\) | \(262623524091319/134454573\) | \(46117918539\) | \([2]\) | \(46080\) | \(0.99778\) | |
37191.a2 | 37191a1 | \([1, 1, 1, -484, -7540]\) | \(-36561310759/46662561\) | \(-16005258423\) | \([2]\) | \(23040\) | \(0.65120\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37191.a have rank \(2\).
Complex multiplication
The elliptic curves in class 37191.a do not have complex multiplication.Modular form 37191.2.a.a
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.