Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 92400.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.g1 | 92400dl4 | \([0, -1, 0, -36801808, -85919117888]\) | \(86129359107301290313/9166294368\) | \(586642839552000000\) | \([2]\) | \(5898240\) | \(2.8372\) | |
92400.g2 | 92400dl2 | \([0, -1, 0, -2305808, -1334925888]\) | \(21184262604460873/216872764416\) | \(13879856922624000000\) | \([2, 2]\) | \(2949120\) | \(2.4906\) | |
92400.g3 | 92400dl3 | \([0, -1, 0, -577808, -3291021888]\) | \(-333345918055753/72923718045024\) | \(-4667117954881536000000\) | \([2]\) | \(5898240\) | \(2.8372\) | |
92400.g4 | 92400dl1 | \([0, -1, 0, -257808, 16754112]\) | \(29609739866953/15259926528\) | \(976635297792000000\) | \([2]\) | \(1474560\) | \(2.1440\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.g have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.g do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.