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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 151725s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151725.bf4 | 151725s1 | \([1, 0, 0, 2069812, 161918367]\) | \(2600176603751/1534698375\) | \(-578810748761724609375\) | \([2]\) | \(5308416\) | \(2.6733\) | \(\Gamma_0(N)\)-optimal |
| 151725.bf3 | 151725s2 | \([1, 0, 0, -8370313, 1299891992]\) | \(171963096231529/97578140625\) | \(36801548472306884765625\) | \([2, 2]\) | \(10616832\) | \(3.0199\) | |
| 151725.bf1 | 151725s3 | \([1, 0, 0, -98646688, 376398230117]\) | \(281486573281608409/610107421875\) | \(230101718639373779296875\) | \([2]\) | \(21233664\) | \(3.3665\) | |
| 151725.bf2 | 151725s4 | \([1, 0, 0, -85135938, -300926373633]\) | \(180945977944161529/992266372125\) | \(374232781617919751953125\) | \([2]\) | \(21233664\) | \(3.3665\) |
Rank
sage: E.rank()
The elliptic curves in class 151725s have rank \(1\).
Complex multiplication
The elliptic curves in class 151725s do not have complex multiplication.Modular form 151725.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
