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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 148225be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148225.be2 | 148225be1 | \([1, 1, 1, -3088, 256906]\) | \(-121\) | \(-26914047015625\) | \([]\) | \(302400\) | \(1.2597\) | \(\Gamma_0(N)\)-optimal |
148225.be1 | 148225be2 | \([1, 1, 1, -4449838, -3614950844]\) | \(-24729001\) | \(-394048562355765625\) | \([]\) | \(3326400\) | \(2.4587\) |
Rank
sage: E.rank()
The elliptic curves in class 148225be have rank \(1\).
Complex multiplication
The elliptic curves in class 148225be do not have complex multiplication.Modular form 148225.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.