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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 94136.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94136.f1 | 94136f4 | \([0, 0, 0, -502619, 137152790]\) | \(1443468546/7\) | \(68097494398976\) | \([2]\) | \(563200\) | \(1.8548\) | |
| 94136.f2 | 94136f3 | \([0, 0, 0, -99179, -9511098]\) | \(11090466/2401\) | \(23357440578848768\) | \([2]\) | \(563200\) | \(1.8548\) | |
| 94136.f3 | 94136f2 | \([0, 0, 0, -31939, 2067630]\) | \(740772/49\) | \(238341230396416\) | \([2, 2]\) | \(281600\) | \(1.5082\) | |
| 94136.f4 | 94136f1 | \([0, 0, 0, 1681, 137842]\) | \(432/7\) | \(-8512186799872\) | \([2]\) | \(140800\) | \(1.1616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94136.f have rank \(1\).
Complex multiplication
The elliptic curves in class 94136.f do not have complex multiplication.Modular form 94136.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
