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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 60840be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.n2 | 60840be1 | \([0, 0, 0, -4563, -338338]\) | \(-78732/325\) | \(-43371774950400\) | \([2]\) | \(129024\) | \(1.3019\) | \(\Gamma_0(N)\)-optimal |
| 60840.n1 | 60840be2 | \([0, 0, 0, -105963, -13256698]\) | \(492983766/845\) | \(225533229742080\) | \([2]\) | \(258048\) | \(1.6485\) |
Rank
sage: E.rank()
The elliptic curves in class 60840be have rank \(0\).
Complex multiplication
The elliptic curves in class 60840be do not have complex multiplication.Modular form 60840.2.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.
