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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 328560.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.s1 | 328560s3 | \([0, -1, 0, -296160, 62094240]\) | \(546718898/405\) | \(2128116112680960\) | \([2]\) | \(3244032\) | \(1.8749\) | |
| 328560.s2 | 328560s4 | \([0, -1, 0, -186640, -30603488]\) | \(136835858/1875\) | \(9852389410560000\) | \([2]\) | \(3244032\) | \(1.8749\) | |
| 328560.s3 | 328560s2 | \([0, -1, 0, -22360, 544000]\) | \(470596/225\) | \(591143364633600\) | \([2, 2]\) | \(1622016\) | \(1.5283\) | |
| 328560.s4 | 328560s1 | \([0, -1, 0, 5020, 62112]\) | \(21296/15\) | \(-9852389410560\) | \([2]\) | \(811008\) | \(1.1817\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 328560.s have rank \(0\).
Complex multiplication
The elliptic curves in class 328560.s do not have complex multiplication.Modular form 328560.2.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.
