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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 9075.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9075.s1 | 9075n2 | \([0, 1, 1, -25208, 1570619]\) | \(-102400/3\) | \(-51901201171875\) | \([]\) | \(42000\) | \(1.4106\) | |
9075.s2 | 9075n1 | \([0, 1, 1, 202, -4801]\) | \(20480/243\) | \(-10762233075\) | \([]\) | \(8400\) | \(0.60585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9075.s have rank \(1\).
Complex multiplication
The elliptic curves in class 9075.s do not have complex multiplication.Modular form 9075.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.