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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 40310bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40310.z1 | 40310bb1 | \([1, 0, 0, -855, 10025]\) | \(-69127969831921/4031000000\) | \(-4031000000\) | \([3]\) | \(19968\) | \(0.59926\) | \(\Gamma_0(N)\)-optimal |
40310.z2 | 40310bb2 | \([1, 0, 0, 4645, 18125]\) | \(11083451457520079/6549956179100\) | \(-6549956179100\) | \([]\) | \(59904\) | \(1.1486\) |
Rank
sage: E.rank()
The elliptic curves in class 40310bb have rank \(0\).
Complex multiplication
The elliptic curves in class 40310bb do not have complex multiplication.Modular form 40310.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.