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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 59290s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.p1 | 59290s1 | \([1, 1, 0, -29768, -2021312]\) | \(-1693700041/32000\) | \(-55119968288000\) | \([]\) | \(217728\) | \(1.4313\) | \(\Gamma_0(N)\)-optimal |
59290.p2 | 59290s2 | \([1, 1, 0, 118457, -9343627]\) | \(106718863559/83886080\) | \(-144493689668894720\) | \([]\) | \(653184\) | \(1.9806\) |
Rank
sage: E.rank()
The elliptic curves in class 59290s have rank \(1\).
Complex multiplication
The elliptic curves in class 59290s do not have complex multiplication.Modular form 59290.2.a.s
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.