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Properties

Label 324870j
Number of curves $2$
Conductor $324870$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 324870j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324870.j1 324870j1 \([1, 1, 0, -22908, 986112]\) \(11301253512121/2899962000\) \(341177629338000\) \([2]\) \(1658880\) \(1.4980\) \(\Gamma_0(N)\)-optimal
324870.j2 324870j2 \([1, 1, 0, 56472, 6399828]\) \(169286748026759/247257562500\) \(-29089604970562500\) \([2]\) \(3317760\) \(1.8446\)  

Rank

sage: E.rank()
 

The elliptic curves in class 324870j have rank \(2\).

Complex multiplication

The elliptic curves in class 324870j do not have complex multiplication.

Modular form 324870.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.