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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 56350bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56350.bz2 | 56350bp1 | \([1, 1, 1, 42237, -15698719]\) | \(4533086375/60669952\) | \(-111527487232000000\) | \([2]\) | \(774144\) | \(1.9519\) | \(\Gamma_0(N)\)-optimal |
56350.bz1 | 56350bp2 | \([1, 1, 1, -741763, -230514719]\) | \(24553362849625/1755162752\) | \(3226455353282000000\) | \([2]\) | \(1548288\) | \(2.2984\) |
Rank
sage: E.rank()
The elliptic curves in class 56350bp have rank \(0\).
Complex multiplication
The elliptic curves in class 56350bp do not have complex multiplication.Modular form 56350.2.a.bp
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.