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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 166093b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166093.b3 | 166093b1 | \([0, -1, 1, -14963, -694008]\) | \(4096000/37\) | \(3346960140253\) | \([]\) | \(202752\) | \(1.2258\) | \(\Gamma_0(N)\)-optimal |
| 166093.b2 | 166093b2 | \([0, -1, 1, -104743, 12669745]\) | \(1404928000/50653\) | \(4581988432006357\) | \([]\) | \(608256\) | \(1.7751\) | |
| 166093.b1 | 166093b3 | \([0, -1, 1, -8409393, 9389117874]\) | \(727057727488000/37\) | \(3346960140253\) | \([]\) | \(1824768\) | \(2.3244\) |
Rank
sage: E.rank()
The elliptic curves in class 166093b have rank \(1\).
Complex multiplication
The elliptic curves in class 166093b do not have complex multiplication.Modular form 166093.2.a.b
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.
