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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 338100.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338100.bo1 | 338100bo1 | \([0, -1, 0, -12413, -521478]\) | \(899022848/13041\) | \(3068521218000\) | \([2]\) | \(663552\) | \(1.1998\) | \(\Gamma_0(N)\)-optimal |
338100.bo2 | 338100bo2 | \([0, -1, 0, -1388, -1425528]\) | \(-78608/233289\) | \(-878278961952000\) | \([2]\) | \(1327104\) | \(1.5464\) |
Rank
sage: E.rank()
The elliptic curves in class 338100.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 338100.bo do not have complex multiplication.Modular form 338100.2.a.bo
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.