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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 50400.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.br1 | 50400dg4 | \([0, 0, 0, -252075, 48712750]\) | \(303735479048/105\) | \(612360000000\) | \([4]\) | \(294912\) | \(1.6176\) | |
| 50400.br2 | 50400dg3 | \([0, 0, 0, -32700, -1136000]\) | \(82881856/36015\) | \(1680315840000000\) | \([2]\) | \(294912\) | \(1.6176\) | |
| 50400.br3 | 50400dg1 | \([0, 0, 0, -15825, 754000]\) | \(601211584/11025\) | \(8037225000000\) | \([2, 2]\) | \(147456\) | \(1.2710\) | \(\Gamma_0(N)\)-optimal |
| 50400.br4 | 50400dg2 | \([0, 0, 0, -75, 2187250]\) | \(-8/354375\) | \(-2066715000000000\) | \([2]\) | \(294912\) | \(1.6176\) |
Rank
sage: E.rank()
The elliptic curves in class 50400.br have rank \(1\).
Complex multiplication
The elliptic curves in class 50400.br do not have complex multiplication.Modular form 50400.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
