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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 18240.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.cg1 | 18240bd4 | \([0, 1, 0, -31518721, 68097944159]\) | \(13209596798923694545921/92340\) | \(24206376960\) | \([2]\) | \(737280\) | \(2.5272\) | |
| 18240.cg2 | 18240bd3 | \([0, 1, 0, -1994241, 1035904095]\) | \(3345930611358906241/165622259047500\) | \(43416881475747840000\) | \([2]\) | \(737280\) | \(2.5272\) | |
| 18240.cg3 | 18240bd2 | \([0, 1, 0, -1969921, 1063536479]\) | \(3225005357698077121/8526675600\) | \(2235216848486400\) | \([2, 2]\) | \(368640\) | \(2.1806\) | |
| 18240.cg4 | 18240bd1 | \([0, 1, 0, -121601, 17017695]\) | \(-758575480593601/40535043840\) | \(-10626018532392960\) | \([2]\) | \(184320\) | \(1.8341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 18240.cg do not have complex multiplication.Modular form 18240.2.a.cg
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
