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Properties

Label 195083m
Number of curves $2$
Conductor $195083$
CM no
Rank $0$
Graph

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

Elliptic curves in class 195083m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195083.m2 195083m1 \([1, 0, 1, -9150, -355117]\) \(-95443993/5887\) \(-5224734170047\) \([2]\) \(367200\) \(1.1948\) \(\Gamma_0(N)\)-optimal
195083.m1 195083m2 \([1, 0, 1, -148495, -22037199]\) \(408023180713/1421\) \(1261142730701\) \([2]\) \(734400\) \(1.5414\)  

Rank

sage: E.rank()
 

The elliptic curves in class 195083m have rank \(0\).

Complex multiplication

The elliptic curves in class 195083m do not have complex multiplication.

Modular form 195083.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 2 q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{12} + 2 q^{13} + q^{14} - 4 q^{15} - q^{16} - 4 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.