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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 61710bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.bj2 | 61710bj1 | \([1, 0, 1, -106483, -5898994]\) | \(75370704203521/35157196800\) | \(62283118720204800\) | \([2]\) | \(645120\) | \(1.9170\) | \(\Gamma_0(N)\)-optimal |
61710.bj1 | 61710bj2 | \([1, 0, 1, -1422963, -653080562]\) | \(179865548102096641/119964240000\) | \(212523968978640000\) | \([2]\) | \(1290240\) | \(2.2636\) |
Rank
sage: E.rank()
The elliptic curves in class 61710bj have rank \(0\).
Complex multiplication
The elliptic curves in class 61710bj do not have complex multiplication.Modular form 61710.2.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 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.