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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 296450.gq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296450.gq1 | 296450gq4 | \([1, 0, 0, -3871047188, -90075862264508]\) | \(1969902499564819009/63690429687500\) | \(207414233505622726440429687500\) | \([2]\) | \(477757440\) | \(4.3993\) | |
| 296450.gq2 | 296450gq2 | \([1, 0, 0, -530055688, 4655337028992]\) | \(5057359576472449/51765560000\) | \(168579706591248981875000000\) | \([2]\) | \(159252480\) | \(3.8500\) | |
| 296450.gq3 | 296450gq1 | \([1, 0, 0, -8303688, 179226620992]\) | \(-19443408769/4249907200\) | \(-13840246465334027200000000\) | \([2]\) | \(79626240\) | \(3.5034\) | \(\Gamma_0(N)\)-optimal |
| 296450.gq4 | 296450gq3 | \([1, 0, 0, 74702312, -4827944317008]\) | \(14156681599871/3100231750000\) | \(-10096213752538837902343750000\) | \([2]\) | \(238878720\) | \(4.0527\) |
Rank
sage: E.rank()
The elliptic curves in class 296450.gq have rank \(0\).
Complex multiplication
The elliptic curves in class 296450.gq do not have complex multiplication.Modular form 296450.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
