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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 333200cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333200.cb2 | 333200cb1 | \([0, -1, 0, 572, -1588]\) | \(27440/17\) | \(-12800211200\) | \([]\) | \(108864\) | \(0.62851\) | \(\Gamma_0(N)\)-optimal |
| 333200.cb1 | 333200cb2 | \([0, -1, 0, -9228, -350468]\) | \(-115431760/4913\) | \(-3699261036800\) | \([]\) | \(326592\) | \(1.1778\) |
Rank
sage: E.rank()
The elliptic curves in class 333200cb have rank \(1\).
Complex multiplication
The elliptic curves in class 333200cb do not have complex multiplication.Modular form 333200.2.a.cb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
