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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 54096bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54096.bb2 | 54096bf1 | \([0, -1, 0, -6848, -218112]\) | \(-25282750375/304704\) | \(-428087181312\) | \([2]\) | \(55296\) | \(1.0436\) | \(\Gamma_0(N)\)-optimal |
54096.bb1 | 54096bf2 | \([0, -1, 0, -109888, -13984256]\) | \(104453838382375/14904\) | \(20939046912\) | \([2]\) | \(110592\) | \(1.3901\) |
Rank
sage: E.rank()
The elliptic curves in class 54096bf have rank \(1\).
Complex multiplication
The elliptic curves in class 54096bf do not have complex multiplication.Modular form 54096.2.a.bf
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.