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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 145200br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.hf4 | 145200br1 | \([0, 1, 0, 661467, -760600062]\) | \(72268906496/606436875\) | \(-268584979177968750000\) | \([2]\) | \(3317760\) | \(2.6013\) | \(\Gamma_0(N)\)-optimal |
| 145200.hf3 | 145200br2 | \([0, 1, 0, -9547908, -10459506312]\) | \(13584145739344/1195803675\) | \(8473756617146700000000\) | \([2]\) | \(6635520\) | \(2.9479\) | |
| 145200.hf2 | 145200br3 | \([0, 1, 0, -47254533, -125144546562]\) | \(-26348629355659264/24169921875\) | \(-10704622741699218750000\) | \([2]\) | \(9953280\) | \(3.1506\) | |
| 145200.hf1 | 145200br4 | \([0, 1, 0, -756238908, -8004796890312]\) | \(6749703004355978704/5671875\) | \(40192290187500000000\) | \([2]\) | \(19906560\) | \(3.4972\) |
Rank
sage: E.rank()
The elliptic curves in class 145200br have rank \(0\).
Complex multiplication
The elliptic curves in class 145200br do not have complex multiplication.Modular form 145200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
