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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 4050.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4050.bh1 | 4050v1 | \([1, -1, 1, -155, 847]\) | \(-35937/4\) | \(-45562500\) | \([]\) | \(1296\) | \(0.20691\) | \(\Gamma_0(N)\)-optimal |
| 4050.bh2 | 4050v2 | \([1, -1, 1, 970, -1403]\) | \(109503/64\) | \(-59049000000\) | \([]\) | \(3888\) | \(0.75622\) |
Rank
sage: E.rank()
The elliptic curves in class 4050.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 4050.bh do not have complex multiplication.Modular form 4050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
