Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 6720.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.br1 | 6720s4 | \([0, 1, 0, -56481, 5147775]\) | \(608119035935048/826875\) | \(27095040000\) | \([2]\) | \(12288\) | \(1.2761\) | |
| 6720.br2 | 6720s3 | \([0, 1, 0, -8961, -221121]\) | \(2428799546888/778248135\) | \(25501634887680\) | \([2]\) | \(12288\) | \(1.2761\) | |
| 6720.br3 | 6720s2 | \([0, 1, 0, -3561, 78039]\) | \(1219555693504/43758225\) | \(179233689600\) | \([2, 2]\) | \(6144\) | \(0.92955\) | |
| 6720.br4 | 6720s1 | \([0, 1, 0, 84, 4410]\) | \(1012048064/130203045\) | \(-8332994880\) | \([2]\) | \(3072\) | \(0.58297\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.br have rank \(1\).
Complex multiplication
The elliptic curves in class 6720.br do not have complex multiplication.Modular form 6720.2.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.
