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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1950.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1950.b1 | 1950a4 | \([1, 1, 0, -29900, -1901250]\) | \(189208196468929/10860320250\) | \(169692503906250\) | \([2]\) | \(6912\) | \(1.4845\) | |
1950.b2 | 1950a2 | \([1, 1, 0, -5150, 139500]\) | \(967068262369/4928040\) | \(77000625000\) | \([2]\) | \(2304\) | \(0.93524\) | |
1950.b3 | 1950a1 | \([1, 1, 0, -150, 4500]\) | \(-24137569/561600\) | \(-8775000000\) | \([2]\) | \(1152\) | \(0.58866\) | \(\Gamma_0(N)\)-optimal |
1950.b4 | 1950a3 | \([1, 1, 0, 1350, -120000]\) | \(17394111071/411937500\) | \(-6436523437500\) | \([2]\) | \(3456\) | \(1.1380\) |
Rank
sage: E.rank()
The elliptic curves in class 1950.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1950.b do not have complex multiplication.Modular form 1950.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.