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Properties

Label 350658l
Number of curves $2$
Conductor $350658$
CM no
Rank $1$
Graph

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

Elliptic curves in class 350658l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.l2 350658l1 \([1, -1, 0, 1523865447, 43221973369581]\) \(303026031242278164433367/800271526601264743872\) \(-1033525043108264851599677035968\) \([2]\) \(530841600\) \(4.4429\) \(\Gamma_0(N)\)-optimal
350658.l1 350658l2 \([1, -1, 0, -13144659633, 488408775842565]\) \(194485894132338991516502953/32757370990533323048376\) \(42305095382923588944107041468344\) \([2]\) \(1061683200\) \(4.7895\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350658l have rank \(1\).

Complex multiplication

The elliptic curves in class 350658l do not have complex multiplication.

Modular form 350658.2.a.l

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