Properties

Label 185020.m
Number of curves $2$
Conductor $185020$
CM no
Rank $2$
Graph

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

Elliptic curves in class 185020.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185020.m1 185020r1 \([0, -1, 0, -736717121, 7696851571970]\) \(4646415367355940880384/38478378125\) \(366205386608100050000\) \([2]\) \(39513600\) \(3.5336\) \(\Gamma_0(N)\)-optimal
185020.m2 185020r2 \([0, -1, 0, -736208316, 7708013329016]\) \(-289799689905740628304/835751962890625\) \(-127263938073310802500000000\) \([2]\) \(79027200\) \(3.8802\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185020.m have rank \(2\).

Complex multiplication

The elliptic curves in class 185020.m do not have complex multiplication.

Modular form 185020.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} + 2 q^{7} + q^{9} - q^{11} - 2 q^{13} - 2 q^{15} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.