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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 223146bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
223146.ef4 | 223146bh1 | \([1, -1, 1, -30659, -3753277]\) | \(-37159393753/49741824\) | \(-4266163295944704\) | \([2]\) | \(1179648\) | \(1.6919\) | \(\Gamma_0(N)\)-optimal |
223146.ef3 | 223146bh2 | \([1, -1, 1, -595139, -176484157]\) | \(271808161065433/147476736\) | \(12648507584461056\) | \([2, 2]\) | \(2359296\) | \(2.0384\) | |
223146.ef2 | 223146bh3 | \([1, -1, 1, -700979, -109296925]\) | \(444142553850073/196663299888\) | \(16867048374453494448\) | \([2]\) | \(4718592\) | \(2.3850\) | |
223146.ef1 | 223146bh4 | \([1, -1, 1, -9520979, -11305221469]\) | \(1112891236915770073/327888\) | \(28121681882448\) | \([2]\) | \(4718592\) | \(2.3850\) |
Rank
sage: E.rank()
The elliptic curves in class 223146bh have rank \(0\).
Complex multiplication
The elliptic curves in class 223146bh do not have complex multiplication.Modular form 223146.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.