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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 76050bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.u1 | 76050bo1 | \([1, -1, 0, -2358342, -2440148684]\) | \(-156116857/186624\) | \(-1734051000395844000000\) | \([]\) | \(4313088\) | \(2.7692\) | \(\Gamma_0(N)\)-optimal |
76050.u2 | 76050bo2 | \([1, -1, 0, 19886283, 45630485941]\) | \(93603087383/150994944\) | \(-1402997115579531264000000\) | \([]\) | \(12939264\) | \(3.3185\) |
Rank
sage: E.rank()
The elliptic curves in class 76050bo have rank \(0\).
Complex multiplication
The elliptic curves in class 76050bo do not have complex multiplication.Modular form 76050.2.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 Cremona 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 Cremona labels.