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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 7056.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.q1 | 7056z5 | \([0, 0, 0, -169491, 26857586]\) | \(3065617154/9\) | \(1580841142272\) | \([2]\) | \(24576\) | \(1.5701\) | |
| 7056.q2 | 7056z3 | \([0, 0, 0, -28371, -1839166]\) | \(28756228/3\) | \(263473523712\) | \([2]\) | \(12288\) | \(1.2235\) | |
| 7056.q3 | 7056z4 | \([0, 0, 0, -10731, 408170]\) | \(1556068/81\) | \(7113785140224\) | \([2, 2]\) | \(12288\) | \(1.2235\) | |
| 7056.q4 | 7056z2 | \([0, 0, 0, -1911, -24010]\) | \(35152/9\) | \(197605142784\) | \([2, 2]\) | \(6144\) | \(0.87691\) | |
| 7056.q5 | 7056z1 | \([0, 0, 0, 294, -2401]\) | \(2048/3\) | \(-4116773808\) | \([2]\) | \(3072\) | \(0.53034\) | \(\Gamma_0(N)\)-optimal |
| 7056.q6 | 7056z6 | \([0, 0, 0, 6909, 1618274]\) | \(207646/6561\) | \(-1152433192716288\) | \([2]\) | \(24576\) | \(1.5701\) |
Rank
sage: E.rank()
The elliptic curves in class 7056.q have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.q do not have complex multiplication.Modular form 7056.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
