Properties

Label 27930u
Number of curves $4$
Conductor $27930$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 27930u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.o3 27930u1 \([1, 1, 0, -144341432, 667414283376]\) \(2826887369998878529467769/2262330000\) \(266160862170000\) \([2]\) \(2703360\) \(2.9715\) \(\Gamma_0(N)\)-optimal
27930.o2 27930u2 \([1, 1, 0, -144342412, 667404766204]\) \(2826944949483509435147449/79970891076562500\) \(9408495364266501562500\) \([2, 2]\) \(5406720\) \(3.3181\)  
27930.o4 27930u3 \([1, 1, 0, -138523662, 723684879954]\) \(-2498661176703400098047449/477389682289643523750\) \(-56164418731694270925663750\) \([2]\) \(10813440\) \(3.6647\)  
27930.o1 27930u4 \([1, 1, 0, -150176842, 610515573046]\) \(3183789741641358436216729/473551070251464843750\) \(55712809864014587402343750\) \([2]\) \(10813440\) \(3.6647\)  

Rank

sage: E.rank()
 

The elliptic curves in class 27930u have rank \(0\).

Complex multiplication

The elliptic curves in class 27930u do not have complex multiplication.

Modular form 27930.2.a.u

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.