Properties

Label 30960.r
Number of curves $2$
Conductor $30960$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.r1 30960u2 \([0, 0, 0, -3123, 46322]\) \(30459021867/9245000\) \(1022423040000\) \([2]\) \(36864\) \(1.0095\)  
30960.r2 30960u1 \([0, 0, 0, -1203, -15502]\) \(1740992427/68800\) \(7608729600\) \([2]\) \(18432\) \(0.66288\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.r have rank \(1\).

Complex multiplication

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

Modular form 30960.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.