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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 37030.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37030.s1 | 37030t4 | \([1, -1, 1, -141607, 20544781]\) | \(2121328796049/120050\) | \(17771708474450\) | \([2]\) | \(202752\) | \(1.6067\) | |
| 37030.s2 | 37030t3 | \([1, -1, 1, -46387, -3581851]\) | \(74565301329/5468750\) | \(809571267968750\) | \([2]\) | \(202752\) | \(1.6067\) | |
| 37030.s3 | 37030t2 | \([1, -1, 1, -9357, 284081]\) | \(611960049/122500\) | \(18134396402500\) | \([2, 2]\) | \(101376\) | \(1.2602\) | |
| 37030.s4 | 37030t1 | \([1, -1, 1, 1223, 25929]\) | \(1367631/2800\) | \(-414500489200\) | \([2]\) | \(50688\) | \(0.91359\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37030.s have rank \(1\).
Complex multiplication
The elliptic curves in class 37030.s do not have complex multiplication.Modular form 37030.2.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.
