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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 23232cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23232.co4 | 23232cg1 | \([0, 1, 0, -15649, -18625]\) | \(912673/528\) | \(245205357821952\) | \([2]\) | \(92160\) | \(1.4506\) | \(\Gamma_0(N)\)-optimal |
| 23232.co2 | 23232cg2 | \([0, 1, 0, -170529, 26961471]\) | \(1180932193/4356\) | \(2022944202031104\) | \([2, 2]\) | \(184320\) | \(1.7971\) | |
| 23232.co3 | 23232cg3 | \([0, 1, 0, -93089, 51633855]\) | \(-192100033/2371842\) | \(-1101493118005936128\) | \([2]\) | \(368640\) | \(2.1437\) | |
| 23232.co1 | 23232cg4 | \([0, 1, 0, -2726049, 1731493311]\) | \(4824238966273/66\) | \(30650669727744\) | \([2]\) | \(368640\) | \(2.1437\) |
Rank
sage: E.rank()
The elliptic curves in class 23232cg have rank \(1\).
Complex multiplication
The elliptic curves in class 23232cg do not have complex multiplication.Modular form 23232.2.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 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.
