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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 47753f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47753.i4 | 47753f1 | \([1, -1, 0, -1931, 14440]\) | \(35937/17\) | \(376794139193\) | \([2]\) | \(37440\) | \(0.91536\) | \(\Gamma_0(N)\)-optimal |
| 47753.i2 | 47753f2 | \([1, -1, 0, -15976, -763653]\) | \(20346417/289\) | \(6405500366281\) | \([2, 2]\) | \(74880\) | \(1.2619\) | |
| 47753.i3 | 47753f3 | \([1, -1, 0, -1931, -2069838]\) | \(-35937/83521\) | \(-1851189605855209\) | \([2]\) | \(149760\) | \(1.6085\) | |
| 47753.i1 | 47753f4 | \([1, -1, 0, -254741, -49423960]\) | \(82483294977/17\) | \(376794139193\) | \([2]\) | \(149760\) | \(1.6085\) |
Rank
sage: E.rank()
The elliptic curves in class 47753f have rank \(0\).
Complex multiplication
The elliptic curves in class 47753f do not have complex multiplication.Modular form 47753.2.a.f
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 Cremona 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 Cremona labels.
