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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 8640q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8640.y1 | 8640q1 | \([0, 0, 0, -10188, 395888]\) | \(-16522921323/4000\) | \(-28311552000\) | \([]\) | \(11520\) | \(0.99435\) | \(\Gamma_0(N)\)-optimal |
8640.y2 | 8640q2 | \([0, 0, 0, 4212, 1394928]\) | \(1601613/163840\) | \(-845378412871680\) | \([]\) | \(34560\) | \(1.5437\) |
Rank
sage: E.rank()
The elliptic curves in class 8640q have rank \(0\).
Complex multiplication
The elliptic curves in class 8640q do not have complex multiplication.Modular form 8640.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.