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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 66150jb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66150.gb2 | 66150jb1 | \([1, -1, 1, -3905, -94153]\) | \(-132651/2\) | \(-99266343750\) | \([]\) | \(81648\) | \(0.91316\) | \(\Gamma_0(N)\)-optimal |
| 66150.gb3 | 66150jb2 | \([1, -1, 1, 14470, -473903]\) | \(9261/8\) | \(-289460658375000\) | \([]\) | \(244944\) | \(1.4625\) | |
| 66150.gb1 | 66150jb3 | \([1, -1, 1, -150905, 29955097]\) | \(-1167051/512\) | \(-166729339224000000\) | \([]\) | \(734832\) | \(2.0118\) |
Rank
sage: E.rank()
The elliptic curves in class 66150jb have rank \(0\).
Complex multiplication
The elliptic curves in class 66150jb do not have complex multiplication.Modular form 66150.2.a.jb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
