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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 18810.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18810.m1 | 18810n2 | \([1, -1, 0, -302499, -63657657]\) | \(4199221866816810289/23034902343750\) | \(16792443808593750\) | \([2]\) | \(184320\) | \(1.9565\) | |
| 18810.m2 | 18810n1 | \([1, -1, 0, -8469, -2087775]\) | \(-92155535561809/2534906137500\) | \(-1847946574237500\) | \([2]\) | \(92160\) | \(1.6099\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18810.m have rank \(1\).
Complex multiplication
The elliptic curves in class 18810.m do not have complex multiplication.Modular form 18810.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
