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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 286650.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.ba1 | 286650ba4 | \([1, -1, 0, -1202168067, -16042599251659]\) | \(143378317900125424089/4976562500000\) | \(6669069711547851562500000\) | \([2]\) | \(141557760\) | \(3.8539\) | |
| 286650.ba2 | 286650ba2 | \([1, -1, 0, -78500067, -226972151659]\) | \(39920686684059609/6492304000000\) | \(8700308288012250000000000\) | \([2, 2]\) | \(70778880\) | \(3.5074\) | |
| 286650.ba3 | 286650ba1 | \([1, -1, 0, -22052067, 36470664341]\) | \(884984855328729/83492864000\) | \(111888423069696000000000\) | \([2]\) | \(35389440\) | \(3.1608\) | \(\Gamma_0(N)\)-optimal |
| 286650.ba4 | 286650ba3 | \([1, -1, 0, 141999933, -1272362651659]\) | \(236293804275620391/658593925444000\) | \(-882578848429610667562500000\) | \([2]\) | \(141557760\) | \(3.8539\) |
Rank
sage: E.rank()
The elliptic curves in class 286650.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 286650.ba do not have complex multiplication.Modular form 286650.2.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 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.
