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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2736.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2736.s1 | 2736t3 | \([0, 0, 0, -14619, 680330]\) | \(115714886617/1539\) | \(4595429376\) | \([2]\) | \(3072\) | \(0.99745\) | |
2736.s2 | 2736t2 | \([0, 0, 0, -939, 10010]\) | \(30664297/3249\) | \(9701462016\) | \([2, 2]\) | \(1536\) | \(0.65087\) | |
2736.s3 | 2736t1 | \([0, 0, 0, -219, -1078]\) | \(389017/57\) | \(170201088\) | \([2]\) | \(768\) | \(0.30430\) | \(\Gamma_0(N)\)-optimal |
2736.s4 | 2736t4 | \([0, 0, 0, 1221, 49322]\) | \(67419143/390963\) | \(-1167409262592\) | \([4]\) | \(3072\) | \(0.99745\) |
Rank
sage: E.rank()
The elliptic curves in class 2736.s have rank \(0\).
Complex multiplication
The elliptic curves in class 2736.s do not have complex multiplication.Modular form 2736.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.