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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 149058s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149058.fk3 | 149058s1 | \([1, -1, 1, -33688661, -75158000823]\) | \(4649101309/6804\) | \(6188284106415643072932\) | \([2]\) | \(11980800\) | \(3.0831\) | \(\Gamma_0(N)\)-optimal |
| 149058.fk4 | 149058s2 | \([1, -1, 1, -23999891, -119288410419]\) | \(-1680914269/5786802\) | \(-5263135632506504433528666\) | \([2]\) | \(23961600\) | \(3.4296\) | |
| 149058.fk1 | 149058s3 | \([1, -1, 1, -1007410046, 12302985896205]\) | \(124318741396429/51631104\) | \(46958838959419919859704832\) | \([2]\) | \(59904000\) | \(3.8878\) | |
| 149058.fk2 | 149058s4 | \([1, -1, 1, -852389726, 16218303114381]\) | \(-75306487574989/81352871712\) | \(-73990988099153493101443041696\) | \([2]\) | \(119808000\) | \(4.2344\) |
Rank
sage: E.rank()
The elliptic curves in class 149058s have rank \(1\).
Complex multiplication
The elliptic curves in class 149058s do not have complex multiplication.Modular form 149058.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
