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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 116160be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116160.b2 | 116160be1 | \([0, -1, 0, -54721, 1091521]\) | \(571305535801/314928000\) | \(9989334761472000\) | \([]\) | \(1161216\) | \(1.7606\) | \(\Gamma_0(N)\)-optimal |
116160.b1 | 116160be2 | \([0, -1, 0, -3381121, 2394103681]\) | \(134766108430924201/283115520\) | \(8980261219860480\) | \([]\) | \(3483648\) | \(2.3099\) |
Rank
sage: E.rank()
The elliptic curves in class 116160be have rank \(0\).
Complex multiplication
The elliptic curves in class 116160be do not have complex multiplication.Modular form 116160.2.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.