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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 35280bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.d1 | 35280bv1 | \([0, 0, 0, -377643, -89177942]\) | \(197723452/375\) | \(11296427329152000\) | \([2]\) | \(430080\) | \(1.9700\) | \(\Gamma_0(N)\)-optimal |
35280.d2 | 35280bv2 | \([0, 0, 0, -254163, -148473038]\) | \(-30138446/140625\) | \(-8472320496864000000\) | \([2]\) | \(860160\) | \(2.3166\) |
Rank
sage: E.rank()
The elliptic curves in class 35280bv have rank \(1\).
Complex multiplication
The elliptic curves in class 35280bv do not have complex multiplication.Modular form 35280.2.a.bv
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.