Properties

Label 30960.bp
Number of curves $4$
Conductor $30960$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.bp1 30960bt4 \([0, 0, 0, -99147, 12016186]\) \(36097320816649/80625\) \(240744960000\) \([4]\) \(90112\) \(1.4291\)  
30960.bp2 30960bt3 \([0, 0, 0, -17067, -618086]\) \(184122897769/51282015\) \(153127276277760\) \([2]\) \(90112\) \(1.4291\)  
30960.bp3 30960bt2 \([0, 0, 0, -6267, 183274]\) \(9116230969/416025\) \(1242243993600\) \([2, 2]\) \(45056\) \(1.0825\)  
30960.bp4 30960bt1 \([0, 0, 0, 213, 10906]\) \(357911/17415\) \(-52000911360\) \([2]\) \(22528\) \(0.73595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 30960.bp do not have complex multiplication.

Modular form 30960.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20})\)  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.