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Properties

Label 203390.m
Number of curves $2$
Conductor $203390$
CM no
Rank $1$
Graph

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

Elliptic curves in class 203390.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203390.m1 203390a1 \([1, 1, 1, -163675, -25798743]\) \(-76711450249/851840\) \(-5384789899660160\) \([]\) \(2201472\) \(1.8334\) \(\Gamma_0(N)\)-optimal
203390.m2 203390a2 \([1, 1, 1, 548190, -133147985]\) \(2882081488391/2883584000\) \(-18228181346287616000\) \([]\) \(6604416\) \(2.3827\)  

Rank

sage: E.rank()
 

The elliptic curves in class 203390.m have rank \(1\).

Complex multiplication

The elliptic curves in class 203390.m do not have complex multiplication.

Modular form 203390.2.a.m

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.