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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 19110.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19110.q1 | 19110q1 | \([1, 1, 0, -4827, 123369]\) | \(105756712489/3478020\) | \(409185574980\) | \([2]\) | \(46080\) | \(1.0014\) | \(\Gamma_0(N)\)-optimal |
19110.q2 | 19110q2 | \([1, 1, 0, 1543, 432951]\) | \(3449795831/688246650\) | \(-80971530125850\) | \([2]\) | \(92160\) | \(1.3480\) |
Rank
sage: E.rank()
The elliptic curves in class 19110.q have rank \(0\).
Complex multiplication
The elliptic curves in class 19110.q do not have complex multiplication.Modular form 19110.2.a.q
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.