Properties

Label 5054.c
Number of curves $6$
Conductor $5054$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5054.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5054.c1 5054c6 \([1, 1, 1, -985718, 376273267]\) \(2251439055699625/25088\) \(1180287062528\) \([2]\) \(42768\) \(1.8853\)  
5054.c2 5054c5 \([1, 1, 1, -61558, 5869939]\) \(-548347731625/1835008\) \(-86329568002048\) \([2]\) \(21384\) \(1.5387\)  
5054.c3 5054c4 \([1, 1, 1, -12823, 452773]\) \(4956477625/941192\) \(44279206830152\) \([2]\) \(14256\) \(1.3360\)  
5054.c4 5054c2 \([1, 1, 1, -3798, -91615]\) \(128787625/98\) \(4610496338\) \([2]\) \(4752\) \(0.78671\)  
5054.c5 5054c1 \([1, 1, 1, -188, -2087]\) \(-15625/28\) \(-1317284668\) \([2]\) \(2376\) \(0.44013\) \(\Gamma_0(N)\)-optimal
5054.c6 5054c3 \([1, 1, 1, 1617, 42677]\) \(9938375/21952\) \(-1032751179712\) \([2]\) \(7128\) \(0.98944\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5054.c have rank \(0\).

Complex multiplication

The elliptic curves in class 5054.c do not have complex multiplication.

Modular form 5054.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{12} + 4 q^{13} + q^{14} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.