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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 15456.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15456.s1 | 15456d3 | \([0, 1, 0, -2577, 49503]\) | \(462248527168/483\) | \(1978368\) | \([2]\) | \(7168\) | \(0.49792\) | |
| 15456.s2 | 15456d2 | \([0, 1, 0, -392, -2040]\) | \(13044257864/4473063\) | \(2290208256\) | \([2]\) | \(7168\) | \(0.49792\) | |
| 15456.s3 | 15456d1 | \([0, 1, 0, -162, 720]\) | \(7392083392/233289\) | \(14930496\) | \([2, 2]\) | \(3584\) | \(0.15135\) | \(\Gamma_0(N)\)-optimal |
| 15456.s4 | 15456d4 | \([0, 1, 0, 48, 2652]\) | \(23393656/5876661\) | \(-3008850432\) | \([2]\) | \(7168\) | \(0.49792\) |
Rank
sage: E.rank()
The elliptic curves in class 15456.s have rank \(1\).
Complex multiplication
The elliptic curves in class 15456.s do not have complex multiplication.Modular form 15456.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
