Properties

Label 3950.g
Number of curves $3$
Conductor $3950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 3950.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3950.g1 3950h3 \([1, 1, 1, -130413, -18181469]\) \(15698803397448457/20709376\) \(323584000000\) \([]\) \(12960\) \(1.4846\)  
3950.g2 3950h2 \([1, 1, 1, -2038, -11469]\) \(59914169497/31554496\) \(493039000000\) \([]\) \(4320\) \(0.93527\)  
3950.g3 3950h1 \([1, 1, 1, -1163, 14781]\) \(11134383337/316\) \(4937500\) \([]\) \(1440\) \(0.38596\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3950.g have rank \(1\).

Complex multiplication

The elliptic curves in class 3950.g do not have complex multiplication.

Modular form 3950.2.a.g

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.