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Properties

Label 30446d
Number of curves $2$
Conductor $30446$
CM no
Rank $1$
Graph

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

Elliptic curves in class 30446d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30446.f2 30446d1 \([1, 0, 1, -67592, 6758038]\) \(34150759536102366457/361740373696\) \(361740373696\) \([3]\) \(107136\) \(1.3740\) \(\Gamma_0(N)\)-optimal
30446.f1 30446d2 \([1, 0, 1, -103927, -1282982]\) \(124137466544322579817/71137289216720896\) \(71137289216720896\) \([]\) \(321408\) \(1.9233\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30446d have rank \(1\).

Complex multiplication

The elliptic curves in class 30446d do not have complex multiplication.

Modular form 30446.2.a.d

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