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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 4080.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4080.s1 | 4080ba2 | \([0, 1, 0, -739096, -244794220]\) | \(10901014250685308569/1040774054400\) | \(4263010526822400\) | \([2]\) | \(48384\) | \(2.0357\) | |
| 4080.s2 | 4080ba1 | \([0, 1, 0, -42776, -4424556]\) | \(-2113364608155289/828431400960\) | \(-3393255018332160\) | \([2]\) | \(24192\) | \(1.6892\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4080.s have rank \(0\).
Complex multiplication
The elliptic curves in class 4080.s do not have complex multiplication.Modular form 4080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
