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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 200400.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.bl1 | 200400k2 | \([0, 1, 0, -8461408, -9096140812]\) | \(1046819248735488409/47650971093750\) | \(3049662150000000000000\) | \([2]\) | \(12386304\) | \(2.8844\) | |
200400.bl2 | 200400k1 | \([0, 1, 0, 286592, -540596812]\) | \(40675641638471/1996889557500\) | \(-127800931680000000000\) | \([2]\) | \(6193152\) | \(2.5378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 200400.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 200400.bl do not have complex multiplication.Modular form 200400.2.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 LMFDB 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 LMFDB labels.