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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 353780be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
353780.be1 | 353780be1 | \([0, 1, 0, -17624140, 28489438900]\) | \(-177953104/125\) | \(-425257502396779808000\) | \([]\) | \(18289152\) | \(2.8946\) | \(\Gamma_0(N)\)-optimal |
353780.be2 | 353780be2 | \([0, 1, 0, 17046300, 121031777348]\) | \(161017136/1953125\) | \(-6644648474949684500000000\) | \([]\) | \(54867456\) | \(3.4439\) |
Rank
sage: E.rank()
The elliptic curves in class 353780be have rank \(1\).
Complex multiplication
The elliptic curves in class 353780be do not have complex multiplication.Modular form 353780.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.