Properties

Label 348075n
Number of curves $2$
Conductor $348075$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348075n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348075.n1 348075n1 \([1, -1, 1, -102380, -12576378]\) \(10418796526321/6390657\) \(72793577390625\) \([2]\) \(1433600\) \(1.6027\) \(\Gamma_0(N)\)-optimal
348075.n2 348075n2 \([1, -1, 1, -83255, -17434128]\) \(-5602762882081/8312741073\) \(-94687316284640625\) \([2]\) \(2867200\) \(1.9492\)  

Rank

sage: E.rank()
 

The elliptic curves in class 348075n have rank \(1\).

Complex multiplication

The elliptic curves in class 348075n do not have complex multiplication.

Modular form 348075.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{7} + 3q^{8} + 4q^{11} - q^{13} + q^{14} - q^{16} + q^{17} + O(q^{20})\)  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.