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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 27225be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27225.o1 | 27225be1 | \([1, -1, 1, -368105, -52123728]\) | \(205379/75\) | \(2014387343834765625\) | \([2]\) | \(405504\) | \(2.2126\) | \(\Gamma_0(N)\)-optimal |
| 27225.o2 | 27225be2 | \([1, -1, 1, 1129270, -369567228]\) | \(5929741/5625\) | \(-151079050787607421875\) | \([2]\) | \(811008\) | \(2.5592\) |
Rank
sage: E.rank()
The elliptic curves in class 27225be have rank \(0\).
Complex multiplication
The elliptic curves in class 27225be do not have complex multiplication.Modular form 27225.2.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.
