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Properties

Label 42630dl
Number of curves $2$
Conductor $42630$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("dl1")
 
E.isogeny_class()
 

Elliptic curves in class 42630dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42630.dh2 42630dl1 \([1, 0, 0, 7790, -325018]\) \(1066931459038991/1552488867810\) \(-76071954522690\) \([]\) \(178752\) \(1.3491\) \(\Gamma_0(N)\)-optimal
42630.dh1 42630dl2 \([1, 0, 0, -2631210, 1642616100]\) \(-41114420704407863185009/1387061010000000\) \(-67965989490000000\) \([7]\) \(1251264\) \(2.3220\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42630dl have rank \(0\).

Complex multiplication

The elliptic curves in class 42630dl do not have complex multiplication.

Modular form 42630.2.a.dl

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.