Properties

Label 30960.o
Number of curves $2$
Conductor $30960$
CM no
Rank $0$
Graph

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

Elliptic curves in class 30960.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.o1 30960bl1 \([0, 0, 0, -22251963, -40299850262]\) \(408076159454905367161/1190206406250000\) \(3553937285760000000000\) \([2]\) \(2027520\) \(3.0057\) \(\Gamma_0(N)\)-optimal
30960.o2 30960bl2 \([0, 0, 0, -13251963, -73198450262]\) \(-86193969101536367161/725294740213012500\) \(-2165718489560211916800000\) \([2]\) \(4055040\) \(3.3523\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{5} + 6q^{11} + 2q^{13} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.