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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 334620e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334620.e1 | 334620e1 | \([0, 0, 0, -1616825028, -7806338417527]\) | \(3778984410690076672/1974078369140625\) | \(244175492023513091894531250000\) | \([2]\) | \(377395200\) | \(4.3308\) | \(\Gamma_0(N)\)-optimal |
| 334620.e2 | 334620e2 | \([0, 0, 0, 6107003097, -60802612714402]\) | \(12727715775275620208/8172570741328125\) | \(-16173959559504058337428260000000\) | \([2]\) | \(754790400\) | \(4.6774\) |
Rank
sage: E.rank()
The elliptic curves in class 334620e have rank \(1\).
Complex multiplication
The elliptic curves in class 334620e do not have complex multiplication.Modular form 334620.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
