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Properties

Label 39270.c
Number of curves $2$
Conductor $39270$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 39270.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39270.c1 39270c2 \([1, 1, 0, -982828, 34815088]\) \(104992182751869695281609/60223351327875600480\) \(60223351327875600480\) \([2]\) \(1351680\) \(2.4851\)  
39270.c2 39270c1 \([1, 1, 0, -708428, 228706128]\) \(39319847421423003352009/99770836591641600\) \(99770836591641600\) \([2]\) \(675840\) \(2.1385\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39270.c have rank \(1\).

Complex multiplication

The elliptic curves in class 39270.c do not have complex multiplication.

Modular form 39270.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.