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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 6630.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6630.i1 | 6630l1 | \([1, 0, 1, -709, 7196]\) | \(39335220262729/23271300\) | \(23271300\) | \([2]\) | \(3584\) | \(0.35810\) | \(\Gamma_0(N)\)-optimal |
6630.i2 | 6630l2 | \([1, 0, 1, -579, 9952]\) | \(-21413157997609/30812096250\) | \(-30812096250\) | \([2]\) | \(7168\) | \(0.70467\) |
Rank
sage: E.rank()
The elliptic curves in class 6630.i have rank \(1\).
Complex multiplication
The elliptic curves in class 6630.i do not have complex multiplication.Modular form 6630.2.a.i
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.