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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 6050.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6050.bj1 | 6050z2 | \([1, 0, 0, -17968563, 29315410367]\) | \(-23178622194826561/1610510\) | \(-44579948532968750\) | \([]\) | \(288000\) | \(2.6487\) | |
6050.bj2 | 6050z1 | \([1, 0, 0, 30187, 8151617]\) | \(109902239/1100000\) | \(-30448704687500000\) | \([]\) | \(57600\) | \(1.8440\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6050.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 6050.bj do not have complex multiplication.Modular form 6050.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.