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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 22800co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.y2 | 22800co1 | \([0, -1, 0, -63208, -6355088]\) | \(-3491055413/175104\) | \(-1400832000000000\) | \([2]\) | \(115200\) | \(1.6672\) | \(\Gamma_0(N)\)-optimal |
| 22800.y1 | 22800co2 | \([0, -1, 0, -1023208, -398035088]\) | \(14809006736693/34656\) | \(277248000000000\) | \([2]\) | \(230400\) | \(2.0138\) |
Rank
sage: E.rank()
The elliptic curves in class 22800co have rank \(0\).
Complex multiplication
The elliptic curves in class 22800co do not have complex multiplication.Modular form 22800.2.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 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.
