Properties

Label 185020m
Number of curves $4$
Conductor $185020$
CM no
Rank $2$
Graph

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

Elliptic curves in class 185020m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185020.o4 185020m1 \([0, -1, 0, -38125, 2819250]\) \(643956736/15125\) \(143947243682000\) \([2]\) \(870912\) \(1.5022\) \(\Gamma_0(N)\)-optimal
185020.o3 185020m2 \([0, -1, 0, -84380, -5303128]\) \(436334416/171875\) \(26172226124000000\) \([2]\) \(1741824\) \(1.8488\)  
185020.o2 185020m3 \([0, -1, 0, -374525, -86982730]\) \(610462990336/8857805\) \(84301263789926480\) \([2]\) \(2612736\) \(2.0515\)  
185020.o1 185020m4 \([0, -1, 0, -5971380, -5614436728]\) \(154639330142416/33275\) \(5066942977606400\) \([2]\) \(5225472\) \(2.3981\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 185020.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{5} - 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.