Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.d1 30960bi2 \([0, 0, 0, -3963, -85462]\) \(2305199161/277350\) \(828162662400\) \([2]\) \(43008\) \(1.0176\)  
30960.d2 30960bi1 \([0, 0, 0, 357, -6838]\) \(1685159/7740\) \(-23111516160\) \([2]\) \(21504\) \(0.67103\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.d

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