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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 230384.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230384.co1 | 230384co1 | \([0, -1, 0, -1195, -15354]\) | \(8869369856/99127\) | \(2111008592\) | \([2]\) | \(195840\) | \(0.60322\) | \(\Gamma_0(N)\)-optimal |
| 230384.co2 | 230384co2 | \([0, -1, 0, -260, -39664]\) | \(-5726576/2000033\) | \(-681483244288\) | \([2]\) | \(391680\) | \(0.94979\) |
Rank
sage: E.rank()
The elliptic curves in class 230384.co have rank \(0\).
Complex multiplication
The elliptic curves in class 230384.co do not have complex multiplication.Modular form 230384.2.a.co
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 LMFDB 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 LMFDB labels.
