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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 33600ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.ez4 | 33600ck1 | \([0, 1, 0, -73508, -31964262]\) | \(-43927191786304/415283203125\) | \(-415283203125000000\) | \([2]\) | \(368640\) | \(2.0630\) | \(\Gamma_0(N)\)-optimal |
| 33600.ez3 | 33600ck2 | \([0, 1, 0, -2026633, -1108136137]\) | \(14383655824793536/45209390625\) | \(2893401000000000000\) | \([2, 2]\) | \(737280\) | \(2.4096\) | |
| 33600.ez2 | 33600ck3 | \([0, 1, 0, -2901633, -59011137]\) | \(5276930158229192/3050936350875\) | \(1562079411648000000000\) | \([4]\) | \(1474560\) | \(2.7562\) | |
| 33600.ez1 | 33600ck4 | \([0, 1, 0, -32401633, -71001011137]\) | \(7347751505995469192/72930375\) | \(37340352000000000\) | \([2]\) | \(1474560\) | \(2.7562\) |
Rank
sage: E.rank()
The elliptic curves in class 33600ck have rank \(0\).
Complex multiplication
The elliptic curves in class 33600ck do not have complex multiplication.Modular form 33600.2.a.ck
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
