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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 224400.gq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.gq1 | 224400cg4 | \([0, 1, 0, -3995408, -3075208812]\) | \(110211585818155849/993794670\) | \(63602858880000000\) | \([2]\) | \(5308416\) | \(2.3895\) | |
| 224400.gq2 | 224400cg2 | \([0, 1, 0, -255408, -45808812]\) | \(28790481449449/2549240100\) | \(163151366400000000\) | \([2, 2]\) | \(2654208\) | \(2.0429\) | |
| 224400.gq3 | 224400cg1 | \([0, 1, 0, -55408, 4191188]\) | \(293946977449/50490000\) | \(3231360000000000\) | \([2]\) | \(1327104\) | \(1.6963\) | \(\Gamma_0(N)\)-optimal |
| 224400.gq4 | 224400cg3 | \([0, 1, 0, 284592, -213208812]\) | \(39829997144951/330164359470\) | \(-21130519006080000000\) | \([2]\) | \(5308416\) | \(2.3895\) |
Rank
sage: E.rank()
The elliptic curves in class 224400.gq have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.gq do not have complex multiplication.Modular form 224400.2.a.gq
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.
