Properties

Label 39270o
Number of curves $4$
Conductor $39270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 39270o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39270.l4 39270o1 \([1, 1, 0, 93013, -160290819]\) \(88991263500189913799/11156306844639559680\) \(-11156306844639559680\) \([2]\) \(1376256\) \(2.3342\) \(\Gamma_0(N)\)-optimal
39270.l3 39270o2 \([1, 1, 0, -3921067, -2895484931]\) \(6667095482374842146270521/240543066599132774400\) \(240543066599132774400\) \([2, 2]\) \(2752512\) \(2.6808\)  
39270.l2 39270o3 \([1, 1, 0, -9883947, 8001081981]\) \(106786168592175009377891641/34113595164994089360000\) \(34113595164994089360000\) \([2]\) \(5505024\) \(3.0274\)  
39270.l1 39270o4 \([1, 1, 0, -62183467, -188764193411]\) \(26591847997770272732680824121/36570473891173918080\) \(36570473891173918080\) \([2]\) \(5505024\) \(3.0274\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39270o have rank \(0\).

Complex multiplication

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

Modular form 39270.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - q^{11} - q^{12} - 6 q^{13} + q^{14} - q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})\) 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.