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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 101568.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101568.bh1 | 101568i2 | \([0, -1, 0, -476897, 126919905]\) | \(15043017316604/243\) | \(193762492416\) | \([2]\) | \(737280\) | \(1.7112\) | |
| 101568.bh2 | 101568i1 | \([0, -1, 0, -29777, 1994577]\) | \(-14647977776/59049\) | \(-11771071414272\) | \([2]\) | \(368640\) | \(1.3646\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101568.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 101568.bh do not have complex multiplication.Modular form 101568.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
