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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 58080.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58080.bj1 | 58080bx4 | \([0, 1, 0, -9841, -378721]\) | \(14526784/15\) | \(108844707840\) | \([2]\) | \(81920\) | \(1.0357\) | |
58080.bj2 | 58080bx3 | \([0, 1, 0, -6816, 212364]\) | \(38614472/405\) | \(367350888960\) | \([2]\) | \(81920\) | \(1.0357\) | |
58080.bj3 | 58080bx1 | \([0, 1, 0, -766, -3016]\) | \(438976/225\) | \(25510478400\) | \([2, 2]\) | \(40960\) | \(0.68911\) | \(\Gamma_0(N)\)-optimal |
58080.bj4 | 58080bx2 | \([0, 1, 0, 2864, -20440]\) | \(2863288/1875\) | \(-1700698560000\) | \([2]\) | \(81920\) | \(1.0357\) |
Rank
sage: E.rank()
The elliptic curves in class 58080.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 58080.bj do not have complex multiplication.Modular form 58080.2.a.bj
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.