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Properties

Label 30030.g
Number of curves $4$
Conductor $30030$
CM no
Rank $1$
Graph

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

Elliptic curves in class 30030.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30030.g1 30030e4 \([1, 1, 0, -243672, -46386444]\) \(1600086203685293756041/505128060937500\) \(505128060937500\) \([2]\) \(245760\) \(1.7968\)  
30030.g2 30030e2 \([1, 1, 0, -17292, -521856]\) \(571871738885758921/216522396090000\) \(216522396090000\) \([2, 2]\) \(122880\) \(1.4502\)  
30030.g3 30030e1 \([1, 1, 0, -7612, 246736]\) \(48787570816576201/1253457004800\) \(1253457004800\) \([2]\) \(61440\) \(1.1036\) \(\Gamma_0(N)\)-optimal
30030.g4 30030e3 \([1, 1, 0, 54208, -3653556]\) \(17615758461429817079/16032362964918300\) \(-16032362964918300\) \([2]\) \(245760\) \(1.7968\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30030.g have rank \(1\).

Complex multiplication

The elliptic curves in class 30030.g do not have complex multiplication.

Modular form 30030.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.