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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 148800bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148800.hf2 | 148800bn1 | \([0, 1, 0, -65633, 6616863]\) | \(-7633736209/230640\) | \(-944701440000000\) | \([2]\) | \(737280\) | \(1.6513\) | \(\Gamma_0(N)\)-optimal |
148800.hf1 | 148800bn2 | \([0, 1, 0, -1057633, 418296863]\) | \(31942518433489/27900\) | \(114278400000000\) | \([2]\) | \(1474560\) | \(1.9979\) |
Rank
sage: E.rank()
The elliptic curves in class 148800bn have rank \(0\).
Complex multiplication
The elliptic curves in class 148800bn do not have complex multiplication.Modular form 148800.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.