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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 222024q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222024.e1 | 222024q1 | \([0, -1, 0, -7008, 69180]\) | \(62500/33\) | \(20100269663232\) | \([2]\) | \(387072\) | \(1.2442\) | \(\Gamma_0(N)\)-optimal |
222024.e2 | 222024q2 | \([0, -1, 0, 26632, 513228]\) | \(1714750/1089\) | \(-1326617797773312\) | \([2]\) | \(774144\) | \(1.5908\) |
Rank
sage: E.rank()
The elliptic curves in class 222024q have rank \(1\).
Complex multiplication
The elliptic curves in class 222024q do not have complex multiplication.Modular form 222024.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.