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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 71478bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71478.o1 | 71478bb1 | \([1, -1, 0, -667737, 169317805]\) | \(960044289625/195182592\) | \(6694069470451089408\) | \([2]\) | \(1290240\) | \(2.3280\) | \(\Gamma_0(N)\)-optimal |
71478.o2 | 71478bb2 | \([1, -1, 0, 1411623, 1012290349]\) | \(9070486526375/18165704832\) | \(-623019137511592407168\) | \([2]\) | \(2580480\) | \(2.6746\) |
Rank
sage: E.rank()
The elliptic curves in class 71478bb have rank \(0\).
Complex multiplication
The elliptic curves in class 71478bb do not have complex multiplication.Modular form 71478.2.a.bb
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.