Properties

Label 3150k
Number of curves 8
Conductor 3150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3150.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.f7 3150k1 [1, -1, 0, -111942, -14382284] [2] 18432 \(\Gamma_0(N)\)-optimal
3150.f6 3150k2 [1, -1, 0, -129942, -9432284] [2, 2] 36864  
3150.f5 3150k3 [1, -1, 0, -331317, 55868341] [2] 55296  
3150.f4 3150k4 [1, -1, 0, -980442, 367339216] [2] 73728  
3150.f8 3150k5 [1, -1, 0, 432558, -69619784] [2] 73728  
3150.f2 3150k6 [1, -1, 0, -4939317, 4226108341] [2, 2] 110592  
3150.f1 3150k7 [1, -1, 0, -79027317, 270424292341] [2] 221184  
3150.f3 3150k8 [1, -1, 0, -4579317, 4867988341] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 3150k have rank \(0\).

Modular form 3150.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{7} - q^{8} - 2q^{13} + q^{14} + q^{16} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.