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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 46800.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.m1 | 46800cb4 | \([0, 0, 0, -14397075, 21026135250]\) | \(261984288445803/42250\) | \(53222832000000000\) | \([2]\) | \(1990656\) | \(2.6117\) | |
| 46800.m2 | 46800cb3 | \([0, 0, 0, -897075, 330635250]\) | \(-63378025803/812500\) | \(-1023516000000000000\) | \([2]\) | \(995328\) | \(2.2651\) | |
| 46800.m3 | 46800cb2 | \([0, 0, 0, -201075, 20787250]\) | \(520300455507/193072360\) | \(333629038080000000\) | \([2]\) | \(663552\) | \(2.0624\) | |
| 46800.m4 | 46800cb1 | \([0, 0, 0, 38925, 2307250]\) | \(3774555693/3515200\) | \(-6074265600000000\) | \([2]\) | \(331776\) | \(1.7158\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.m have rank \(0\).
Complex multiplication
The elliptic curves in class 46800.m do not have complex multiplication.Modular form 46800.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
