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Properties

Label 102960.ep
Number of curves $4$
Conductor $102960$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ep1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 102960.ep have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(11\)\(1 + T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 102960.ep do not have complex multiplication.

Modular form 102960.2.a.ep

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{7} - q^{11} + q^{13} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 102960.ep

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.ep1 102960eg4 \([0, 0, 0, -511102398387, -140640367301390734]\) \(4944928228995290413834018379264689/189679641808585500000\) \(566380375566167365632000000\) \([2]\) \(464486400\) \(5.0736\)  
102960.ep2 102960eg3 \([0, 0, 0, -31942398387, -2197722653390734]\) \(-1207087636168285491836819264689/236446260657750000000000\) \(-706024751183870976000000000000\) \([2]\) \(232243200\) \(4.7270\)  
102960.ep3 102960eg2 \([0, 0, 0, -6360994227, -189639474165646]\) \(9532597152396244075685450929/313550122650789880627200\) \(936255649433296170914729164800\) \([2]\) \(154828800\) \(4.5243\)  
102960.ep4 102960eg1 \([0, 0, 0, 127069773, -10217254696846]\) \(75991146714893572533071/15147028085515223040000\) \(-45228783510899087753871360000\) \([2]\) \(77414400\) \(4.1777\) \(\Gamma_0(N)\)-optimal