Properties

Label 51480bu
Number of curves $4$
Conductor $51480$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51480bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51480.bb4 51480bu1 \([0, 0, 0, -822207, -390626494]\) \(-329381898333928144/162600887109375\) \(-30345227955900000000\) \([4]\) \(1376256\) \(2.4435\) \(\Gamma_0(N)\)-optimal
51480.bb3 51480bu2 \([0, 0, 0, -14434707, -21106128994]\) \(445574312599094932036/61129333175625\) \(45632802698271360000\) \([2, 2]\) \(2752512\) \(2.7901\)  
51480.bb2 51480bu3 \([0, 0, 0, -15721707, -17118745594]\) \(287849398425814280018/81784533026485575\) \(122103653532278751590400\) \([2]\) \(5505024\) \(3.1367\)  
51480.bb1 51480bu4 \([0, 0, 0, -230947707, -1350885672394]\) \(912446049969377120252018/17177299425\) \(25645570623129600\) \([2]\) \(5505024\) \(3.1367\)  

Rank

sage: E.rank()
 

The elliptic curves in class 51480bu have rank \(0\).

Complex multiplication

The elliptic curves in class 51480bu do not have complex multiplication.

Modular form 51480.2.a.bu

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} + q^{11} + q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.