Properties

Label 77760.dm
Number of curves 22
Conductor 7776077760
CM no
Rank 11
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dm1") E.isogeny_class()
 

Elliptic curves in class 77760.dm

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77760.dm1 77760br2 [0,0,0,700812,225813744][0, 0, 0, -700812, 225813744] 819699324507/80819699324507/80 37150418534403715041853440 [][] 497664497664 1.84501.8450  
77760.dm2 77760br1 [0,0,0,9612,236784][0, 0, 0, -9612, 236784] 1541767203/5120001541767203/512000 3261490790400032614907904000 [][] 165888165888 1.29571.2957 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 77760.dm have rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
551T1 - T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 1+T+7T2 1 + T + 7 T^{2} 1.7.b
1111 1+3T+11T2 1 + 3 T + 11 T^{2} 1.11.d
1313 14T+13T2 1 - 4 T + 13 T^{2} 1.13.ae
1717 13T+17T2 1 - 3 T + 17 T^{2} 1.17.ad
1919 14T+19T2 1 - 4 T + 19 T^{2} 1.19.ae
2323 16T+23T2 1 - 6 T + 23 T^{2} 1.23.ag
2929 1+29T2 1 + 29 T^{2} 1.29.a
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 77760.dm do not have complex multiplication.

Modular form 77760.2.a.dm

Copy content sage:E.q_eigenform(10)
 
q+q5q73q11+4q13+3q17+4q19+O(q20)q + q^{5} - q^{7} - 3 q^{11} + 4 q^{13} + 3 q^{17} + 4 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.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.