Properties

Label 6930.i
Number of curves 22
Conductor 69306930
CM no
Rank 00
Graph

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Copy content sage:E = EllipticCurve("i1") E.isogeny_class()
 

Elliptic curves in class 6930.i

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.i1 6930c1 [1,1,0,2094,33580][1, -1, 0, -2094, -33580] 51603494067/433664051603494067/4336640 8535808512085358085120 [2][2] 76807680 0.839280.83928 Γ0(N)\Gamma_0(N)-optimal
6930.i2 6930c2 [1,1,0,2226,157132][1, -1, 0, 2226, -157132] 61958108493/57392720061958108493/573927200 11296609077600-11296609077600 [2][2] 1536015360 1.18591.1859  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 6930.i have rank 00.

Complex multiplication

The elliptic curves in class 6930.i do not have complex multiplication.

Modular form 6930.2.a.i

Copy content sage:E.q_eigenform(10)
 
qq2+q4+q5q7q8q10q11+2q13+q14+q162q19+O(q20)q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - q^{11} + 2 q^{13} + q^{14} + q^{16} - 2 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.