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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 70560bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.d3 | 70560bb1 | \([0, 0, 0, -99813, 11896612]\) | \(20034997696/455625\) | \(2500940088360000\) | \([2, 2]\) | \(442368\) | \(1.7413\) | \(\Gamma_0(N)\)-optimal |
70560.d4 | 70560bb2 | \([0, 0, 0, 10437, 36746962]\) | \(2863288/13286025\) | \(-583419303812620800\) | \([2]\) | \(884736\) | \(2.0879\) | |
70560.d2 | 70560bb3 | \([0, 0, 0, -218883, -21943082]\) | \(26410345352/10546875\) | \(463137053400000000\) | \([2]\) | \(884736\) | \(2.0879\) | |
70560.d1 | 70560bb4 | \([0, 0, 0, -1588188, 770372512]\) | \(1261112198464/675\) | \(237126171340800\) | \([2]\) | \(884736\) | \(2.0879\) |
Rank
sage: E.rank()
The elliptic curves in class 70560bb have rank \(1\).
Complex multiplication
The elliptic curves in class 70560bb do not have complex multiplication.Modular form 70560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.