Properties

Label 278850.iv
Number of curves $2$
Conductor $278850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("iv1")
 
E.isogeny_class()
 

Elliptic curves in class 278850.iv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
278850.iv1 278850iv2 \([1, 0, 0, -68160830813, -6849372486091383]\) \(464352938845529653759213009/2445173327025000\) \(184412259710065831640625000\) \([2]\) \(650280960\) \(4.6567\)  
278850.iv2 278850iv1 \([1, 0, 0, -4257705813, -107145476716383]\) \(-113180217375258301213009/260161419375000000\) \(-19621085632687880859375000000\) \([2]\) \(325140480\) \(4.3101\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 278850.iv have rank \(1\).

Complex multiplication

The elliptic curves in class 278850.iv do not have complex multiplication.

Modular form 278850.2.a.iv

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