Properties

Label 30960e
Number of curves $4$
Conductor $30960$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.m4 30960e1 \([0, 0, 0, -8103, 358022]\) \(-315278049616/114259815\) \(-21323623714560\) \([2]\) \(67584\) \(1.2681\) \(\Gamma_0(N)\)-optimal
30960.m3 30960e2 \([0, 0, 0, -139323, 20014778]\) \(400649568576484/33698025\) \(25155440870400\) \([2, 2]\) \(135168\) \(1.6147\)  
30960.m2 30960e3 \([0, 0, 0, -149043, 17061842]\) \(245245463376482/57692266875\) \(86134092906240000\) \([2]\) \(270336\) \(1.9613\)  
30960.m1 30960e4 \([0, 0, 0, -2229123, 1281000098]\) \(820480625548035842/5805\) \(8666818560\) \([2]\) \(270336\) \(1.9613\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{11} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.