Properties

Label 324870l
Number of curves $2$
Conductor $324870$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 324870l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324870.l1 324870l1 \([1, 1, 0, -683, 3837]\) \(102963870703/38188800\) \(13098758400\) \([2]\) \(258048\) \(0.64129\) \(\Gamma_0(N)\)-optimal
324870.l2 324870l2 \([1, 1, 0, 2117, 30157]\) \(3056832103697/2848407120\) \(-977003642160\) \([2]\) \(516096\) \(0.98787\)  

Rank

sage: E.rank()
 

The elliptic curves in class 324870l have rank \(1\).

Complex multiplication

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

Modular form 324870.2.a.l

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