Properties

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

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 27930.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.db1 27930cw4 \([1, 0, 0, -24131521, -45629351755]\) \(13209596798923694545921/92340\) \(10863708660\) \([2]\) \(1105920\) \(2.4604\)  
27930.db2 27930cw3 \([1, 0, 0, -1526841, -694547379]\) \(3345930611358906241/165622259047500\) \(19485293154679327500\) \([2]\) \(1105920\) \(2.4604\)  
27930.db3 27930cw2 \([1, 0, 0, -1508221, -713051935]\) \(3225005357698077121/8526675600\) \(1003154857664400\) \([2, 2]\) \(552960\) \(2.1139\)  
27930.db4 27930cw1 \([1, 0, 0, -93101, -11435439]\) \(-758575480593601/40535043840\) \(-4768907372732160\) \([2]\) \(276480\) \(1.7673\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 27930.2.a.db

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.