Properties

Label 391460.m
Number of curves 22
Conductor 391460391460
CM no
Rank 00
Graph

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

Elliptic curves in class 391460.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
391460.m1 391460m2 [0,1,0,6359285,6170368775][0, 1, 0, -6359285, 6170368775] 750484394082304/578125750484394082304/578125 2190931157200000021909311572000000 [][] 54743045474304 2.44332.4433  
391460.m2 391460m1 [0,1,0,95925,4404023][0, 1, 0, -95925, 4404023] 2575826944/12663252575826944/1266325 4799015606730880047990156067308800 [][] 18247681824768 1.89401.8940 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 391460.m have rank 00.

Complex multiplication

The elliptic curves in class 391460.m do not have complex multiplication.

Modular form 391460.2.a.m

sage: E.q_eigenform(10)
 
q+q3+q5+q72q9+3q114q13+q15+4q19+O(q20)q + q^{3} + q^{5} + q^{7} - 2 q^{9} + 3 q^{11} - 4 q^{13} + q^{15} + 4 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.