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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8820.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8820.g1 | 8820j3 | \([0, 0, 0, -18228, -947023]\) | \(488095744/125\) | \(171532242000\) | \([2]\) | \(12960\) | \(1.1416\) | |
| 8820.g2 | 8820j4 | \([0, 0, 0, -16023, -1184722]\) | \(-20720464/15625\) | \(-343064484000000\) | \([2]\) | \(25920\) | \(1.4882\) | |
| 8820.g3 | 8820j1 | \([0, 0, 0, -588, 3773]\) | \(16384/5\) | \(6861289680\) | \([2]\) | \(4320\) | \(0.59231\) | \(\Gamma_0(N)\)-optimal |
| 8820.g4 | 8820j2 | \([0, 0, 0, 1617, 25382]\) | \(21296/25\) | \(-548903174400\) | \([2]\) | \(8640\) | \(0.93888\) |
Rank
sage: E.rank()
The elliptic curves in class 8820.g have rank \(0\).
Complex multiplication
The elliptic curves in class 8820.g do not have complex multiplication.Modular form 8820.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
