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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 43120.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43120.i1 | 43120bv4 | \([0, 1, 0, -2759696, -1755865196]\) | \(4823468134087681/30382271150\) | \(14640921880683929600\) | \([2]\) | \(1327104\) | \(2.5149\) | |
| 43120.i2 | 43120bv2 | \([0, 1, 0, -211696, 35810004]\) | \(2177286259681/105875000\) | \(51020135936000000\) | \([2]\) | \(442368\) | \(1.9656\) | |
| 43120.i3 | 43120bv3 | \([0, 1, 0, -70576, -59568300]\) | \(-80677568161/3131816380\) | \(-1509191947430379520\) | \([2]\) | \(663552\) | \(2.1683\) | |
| 43120.i4 | 43120bv1 | \([0, 1, 0, 7824, 2179540]\) | \(109902239/4312000\) | \(-2077910990848000\) | \([2]\) | \(221184\) | \(1.6190\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43120.i have rank \(0\).
Complex multiplication
The elliptic curves in class 43120.i do not have complex multiplication.Modular form 43120.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
