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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 7056.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7056.bx1 | 7056bi1 | \([0, 0, 0, -1491, 22162]\) | \(-67645179/8\) | \(-43352064\) | \([]\) | \(3456\) | \(0.49093\) | \(\Gamma_0(N)\)-optimal |
7056.bx2 | 7056bi2 | \([0, 0, 0, 189, 68418]\) | \(189/512\) | \(-2022633897984\) | \([]\) | \(10368\) | \(1.0402\) |
Rank
sage: E.rank()
The elliptic curves in class 7056.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.bx do not have complex multiplication.Modular form 7056.2.a.bx
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.