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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 3120.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3120.s1 | 3120k3 | \([0, 1, 0, -8320, -294892]\) | \(31103978031362/195\) | \(399360\) | \([2]\) | \(3072\) | \(0.68038\) | |
| 3120.s2 | 3120k4 | \([0, 1, 0, -720, -972]\) | \(20183398562/11567205\) | \(23689635840\) | \([4]\) | \(3072\) | \(0.68038\) | |
| 3120.s3 | 3120k2 | \([0, 1, 0, -520, -4732]\) | \(15214885924/38025\) | \(38937600\) | \([2, 2]\) | \(1536\) | \(0.33381\) | |
| 3120.s4 | 3120k1 | \([0, 1, 0, -20, -132]\) | \(-3631696/24375\) | \(-6240000\) | \([2]\) | \(768\) | \(-0.012768\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3120.s have rank \(0\).
Complex multiplication
The elliptic curves in class 3120.s do not have complex multiplication.Modular form 3120.2.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.
