Properties

Label 3150l
Number of curves 6
Conductor 3150
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("3150.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.i5 3150l1 [1, -1, 0, -117, -959] [2] 1152 \(\Gamma_0(N)\)-optimal
3150.i4 3150l2 [1, -1, 0, -2367, -43709] [2] 2304  
3150.i6 3150l3 [1, -1, 0, 1008, 20416] [2] 3456  
3150.i3 3150l4 [1, -1, 0, -7992, 227416] [2] 6912  
3150.i2 3150l5 [1, -1, 0, -38367, 2910541] [2] 10368  
3150.i1 3150l6 [1, -1, 0, -614367, 185502541] [2] 20736  

Rank

sage: E.rank()
 

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

Modular form 3150.2.a.i

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.