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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 76440br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.h3 | 76440br1 | \([0, -1, 0, -12756, -453564]\) | \(7622072656/1404585\) | \(42303493290240\) | \([2]\) | \(196608\) | \(1.3330\) | \(\Gamma_0(N)\)-optimal |
| 76440.h2 | 76440br2 | \([0, -1, 0, -60776, 5366460]\) | \(206081497444/16769025\) | \(2020207638758400\) | \([2, 2]\) | \(393216\) | \(1.6796\) | |
| 76440.h4 | 76440br3 | \([0, -1, 0, 62704, 24283596]\) | \(113157757438/1124589375\) | \(-270964357896960000\) | \([2]\) | \(786432\) | \(2.0262\) | |
| 76440.h1 | 76440br4 | \([0, -1, 0, -952576, 358162540]\) | \(396738988420322/2985255\) | \(719282719733760\) | \([2]\) | \(786432\) | \(2.0262\) |
Rank
sage: E.rank()
The elliptic curves in class 76440br have rank \(1\).
Complex multiplication
The elliptic curves in class 76440br do not have complex multiplication.Modular form 76440.2.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.
