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Properties

Label 30030d
Number of curves $2$
Conductor $30030$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 30030d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30030.d2 30030d1 \([1, 1, 0, 33, 369]\) \(3789119879/56756700\) \(-56756700\) \([2]\) \(11264\) \(0.16850\) \(\Gamma_0(N)\)-optimal
30030.d1 30030d2 \([1, 1, 0, -597, 5031]\) \(23592983745241/1610358750\) \(1610358750\) \([2]\) \(22528\) \(0.51507\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30030.2.a.d

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