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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 48400br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48400.bt4 | 48400br1 | \([0, 0, 0, 39325, 2329250]\) | \(59319/55\) | \(-6235894720000000\) | \([2]\) | \(184320\) | \(1.7180\) | \(\Gamma_0(N)\)-optimal |
| 48400.bt3 | 48400br2 | \([0, 0, 0, -202675, 20963250]\) | \(8120601/3025\) | \(342974209600000000\) | \([2, 2]\) | \(368640\) | \(2.0646\) | |
| 48400.bt2 | 48400br3 | \([0, 0, 0, -1412675, -631226750]\) | \(2749884201/73205\) | \(8299975872320000000\) | \([2]\) | \(737280\) | \(2.4111\) | |
| 48400.bt1 | 48400br4 | \([0, 0, 0, -2864675, 1865729250]\) | \(22930509321/6875\) | \(779486840000000000\) | \([2]\) | \(737280\) | \(2.4111\) |
Rank
sage: E.rank()
The elliptic curves in class 48400br have rank \(1\).
Complex multiplication
The elliptic curves in class 48400br do not have complex multiplication.Modular form 48400.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
