Properties

Label 60984.i
Number of curves $2$
Conductor $60984$
CM no
Rank $1$
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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.i1 60984v2 \([0, 0, 0, -24820851, 33383409950]\) \(1278763167594532/375974556419\) \(497212515096700767243264\) \([2]\) \(5529600\) \(3.2528\)  
60984.i2 60984v1 \([0, 0, 0, 4168329, 3472374026]\) \(24226243449392/29774625727\) \(-9843961706338262646528\) \([2]\) \(2764800\) \(2.9062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 60984.i have rank \(1\).

Complex multiplication

The elliptic curves in class 60984.i do not have complex multiplication.

Modular form 60984.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{7} + 4q^{17} - 4q^{19} + O(q^{20})\)  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 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.