Properties

Label 56925m
Number of curves $6$
Conductor $56925$
CM no
Rank $0$
Graph

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

Elliptic curves in class 56925m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56925.l6 56925m1 \([1, -1, 1, 6970, 654972]\) \(3288008303/18259263\) \(-207984417609375\) \([2]\) \(131072\) \(1.4294\) \(\Gamma_0(N)\)-optimal
56925.l5 56925m2 \([1, -1, 1, -84155, 8491722]\) \(5786435182177/627352209\) \(7145933755640625\) \([2, 2]\) \(262144\) \(1.7760\)  
56925.l4 56925m3 \([1, -1, 1, -317030, -59507778]\) \(309368403125137/44372288367\) \(505428097180359375\) \([2]\) \(524288\) \(2.1226\)  
56925.l2 56925m4 \([1, -1, 1, -1309280, 576949722]\) \(21790813729717297/304746849\) \(3471257076890625\) \([2, 2]\) \(524288\) \(2.1226\)  
56925.l3 56925m5 \([1, -1, 1, -1272155, 611178972]\) \(-19989223566735457/2584262514273\) \(-29436365201640890625\) \([2]\) \(1048576\) \(2.4691\)  
56925.l1 56925m6 \([1, -1, 1, -20948405, 36909330972]\) \(89254274298475942657/17457\) \(198846140625\) \([2]\) \(1048576\) \(2.4691\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56925m have rank \(0\).

Complex multiplication

The elliptic curves in class 56925m do not have complex multiplication.

Modular form 56925.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{8} - q^{11} + 2 q^{13} - q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.