Properties

Label 7056.q
Number of curves $6$
Conductor $7056$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: 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)
 
\(q - 2q^{5} + 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display

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.