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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 37026ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.bk4 | 37026ba1 | \([1, -1, 1, -3290, 45785]\) | \(3048625/1088\) | \(1405117150272\) | \([2]\) | \(51840\) | \(1.0319\) | \(\Gamma_0(N)\)-optimal |
| 37026.bk3 | 37026ba2 | \([1, -1, 1, -46850, 3913913]\) | \(8805624625/2312\) | \(2985873944328\) | \([2]\) | \(103680\) | \(1.3784\) | |
| 37026.bk2 | 37026ba3 | \([1, -1, 1, -112190, -14433559]\) | \(120920208625/19652\) | \(25379928526788\) | \([2]\) | \(155520\) | \(1.5812\) | |
| 37026.bk1 | 37026ba4 | \([1, -1, 1, -123080, -11454055]\) | \(159661140625/48275138\) | \(62345794426054722\) | \([2]\) | \(311040\) | \(1.9277\) |
Rank
sage: E.rank()
The elliptic curves in class 37026ba have rank \(0\).
Complex multiplication
The elliptic curves in class 37026ba do not have complex multiplication.Modular form 37026.2.a.ba
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 Cremona 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 Cremona labels.
