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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 47096a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47096.i4 | 47096a1 | \([0, 0, 0, 841, 48778]\) | \(432/7\) | \(-1065923391232\) | \([2]\) | \(48384\) | \(0.98847\) | \(\Gamma_0(N)\)-optimal |
| 47096.i3 | 47096a2 | \([0, 0, 0, -15979, 731670]\) | \(740772/49\) | \(29845854954496\) | \([2, 2]\) | \(96768\) | \(1.3350\) | |
| 47096.i2 | 47096a3 | \([0, 0, 0, -49619, -3365682]\) | \(11090466/2401\) | \(2924893785540608\) | \([2]\) | \(193536\) | \(1.6816\) | |
| 47096.i1 | 47096a4 | \([0, 0, 0, -251459, 48534110]\) | \(1443468546/7\) | \(8527387129856\) | \([2]\) | \(193536\) | \(1.6816\) |
Rank
sage: E.rank()
The elliptic curves in class 47096a have rank \(1\).
Complex multiplication
The elliptic curves in class 47096a do not have complex multiplication.Modular form 47096.2.a.a
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.
