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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 134640be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.fd2 | 134640be1 | \([0, 0, 0, 3813, 79306]\) | \(2053225511/2098140\) | \(-6265012469760\) | \([2]\) | \(196608\) | \(1.1423\) | \(\Gamma_0(N)\)-optimal |
| 134640.fd1 | 134640be2 | \([0, 0, 0, -20667, 730474]\) | \(326940373369/112003650\) | \(334441106841600\) | \([2]\) | \(393216\) | \(1.4889\) |
Rank
sage: E.rank()
The elliptic curves in class 134640be have rank \(1\).
Complex multiplication
The elliptic curves in class 134640be do not have complex multiplication.Modular form 134640.2.a.be
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.
