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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2800.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2800.g1 | 2800v6 | \([0, 1, 0, -1092208, 438981588]\) | \(2251439055699625/25088\) | \(1605632000000\) | \([2]\) | \(20736\) | \(1.9110\) | |
| 2800.g2 | 2800v5 | \([0, 1, 0, -68208, 6853588]\) | \(-548347731625/1835008\) | \(-117440512000000\) | \([2]\) | \(10368\) | \(1.5644\) | |
| 2800.g3 | 2800v4 | \([0, 1, 0, -14208, 529588]\) | \(4956477625/941192\) | \(60236288000000\) | \([2]\) | \(6912\) | \(1.3617\) | |
| 2800.g4 | 2800v2 | \([0, 1, 0, -4208, -106412]\) | \(128787625/98\) | \(6272000000\) | \([2]\) | \(2304\) | \(0.81236\) | |
| 2800.g5 | 2800v1 | \([0, 1, 0, -208, -2412]\) | \(-15625/28\) | \(-1792000000\) | \([2]\) | \(1152\) | \(0.46578\) | \(\Gamma_0(N)\)-optimal |
| 2800.g6 | 2800v3 | \([0, 1, 0, 1792, 49588]\) | \(9938375/21952\) | \(-1404928000000\) | \([2]\) | \(3456\) | \(1.0151\) |
Rank
sage: E.rank()
The elliptic curves in class 2800.g have rank \(1\).
Complex multiplication
The elliptic curves in class 2800.g do not have complex multiplication.Modular form 2800.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
