Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 7056.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7056.x1 | 7056br4 | \([0, 0, 0, -806295, 278668978]\) | \(2640279346000/3087\) | \(67778563974912\) | \([2]\) | \(55296\) | \(1.9371\) | |
7056.x2 | 7056br3 | \([0, 0, 0, -49980, 4429159]\) | \(-10061824000/352947\) | \(-484334321737392\) | \([2]\) | \(27648\) | \(1.5905\) | |
7056.x3 | 7056br2 | \([0, 0, 0, -12495, 172186]\) | \(9826000/5103\) | \(112042115958528\) | \([2]\) | \(18432\) | \(1.3878\) | |
7056.x4 | 7056br1 | \([0, 0, 0, 2940, 20923]\) | \(2048000/1323\) | \(-1815497249328\) | \([2]\) | \(9216\) | \(1.0412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.x have rank \(0\).
Complex multiplication
The elliptic curves in class 7056.x do not have complex multiplication.Modular form 7056.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.