Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.t1 30960t2 \([0, 0, 0, -1421523, 597112722]\) \(3940344055317123/369800000000\) \(29813855846400000000\) \([2]\) \(663552\) \(2.4751\)  
30960.t2 30960t1 \([0, 0, 0, -315603, -57813102]\) \(43121696645763/7045120000\) \(567988621148160000\) \([2]\) \(331776\) \(2.1285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2q^{7} - 2q^{11} + 2q^{13} + 8q^{19} + O(q^{20})\)  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.