Properties

Label 8100.m
Number of curves 22
Conductor 81008100
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 8100.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8100.m1 8100h2 [0,0,0,16200,121500][0, 0, 0, -16200, -121500] 221184/125221184/125 265720500000000265720500000000 [][] 3110431104 1.45781.4578  
8100.m2 8100h1 [0,0,0,10200,396500][0, 0, 0, -10200, 396500] 362225664/5362225664/5 16200000001620000000 [][] 1036810368 0.908490.90849 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8100.m have rank 00.

Complex multiplication

The elliptic curves in class 8100.m do not have complex multiplication.

Modular form 8100.2.a.m

sage: E.q_eigenform(10)
 
q+4q73q11+4q13+5q19+O(q20)q + 4 q^{7} - 3 q^{11} + 4 q^{13} + 5 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

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

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

The vertices are labelled with LMFDB labels.