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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 5040.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.bh1 | 5040h1 | \([0, 0, 0, -27, 26]\) | \(78732/35\) | \(967680\) | \([2]\) | \(768\) | \(-0.15586\) | \(\Gamma_0(N)\)-optimal |
5040.bh2 | 5040h2 | \([0, 0, 0, 93, 194]\) | \(1608714/1225\) | \(-67737600\) | \([2]\) | \(1536\) | \(0.19072\) |
Rank
sage: E.rank()
The elliptic curves in class 5040.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 5040.bh do not have complex multiplication.Modular form 5040.2.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.