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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 56350bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56350.bf2 | 56350bl1 | \([1, 0, 0, -1863, 24877]\) | \(243135625/48668\) | \(143143538300\) | \([]\) | \(54432\) | \(0.85669\) | \(\Gamma_0(N)\)-optimal |
56350.bf1 | 56350bl2 | \([1, 0, 0, -142738, 20744772]\) | \(109348914285625/1472\) | \(4329483200\) | \([]\) | \(163296\) | \(1.4060\) |
Rank
sage: E.rank()
The elliptic curves in class 56350bl have rank \(1\).
Complex multiplication
The elliptic curves in class 56350bl do not have complex multiplication.Modular form 56350.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.