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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 274890.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 274890.f1 | 274890f4 | \([1, 1, 0, -118450273, 372888305077]\) | \(1562225332123379392365961/393363080510106009600\) | \(46278773058933461923430400\) | \([2]\) | \(99532800\) | \(3.6346\) | |
| 274890.f2 | 274890f2 | \([1, 1, 0, -40668898, -99806728748]\) | \(63229930193881628103961/26218934428500000\) | \(3084631416578596500000\) | \([2]\) | \(33177600\) | \(3.0853\) | |
| 274890.f3 | 274890f1 | \([1, 1, 0, -2150978, -2055951372]\) | \(-9354997870579612441/10093752054144000\) | \(-1187519835417987456000\) | \([2]\) | \(16588800\) | \(2.7387\) | \(\Gamma_0(N)\)-optimal |
| 274890.f4 | 274890f3 | \([1, 1, 0, 18028447, 37123358133]\) | \(5508208700580085578359/8246033269590589440\) | \(-970137568134063257026560\) | \([2]\) | \(49766400\) | \(3.2880\) |
Rank
sage: E.rank()
The elliptic curves in class 274890.f have rank \(0\).
Complex multiplication
The elliptic curves in class 274890.f do not have complex multiplication.Modular form 274890.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
