Properties

Label 270480.eg
Number of curves $2$
Conductor $270480$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eg1")
 
E.isogeny_class()
 

Elliptic curves in class 270480.eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.eg1 270480eg1 \([0, -1, 0, -51720300, 137915979552]\) \(508017439289666674384/21234429931640625\) \(639541618439062500000000\) \([2]\) \(41287680\) \(3.3328\) \(\Gamma_0(N)\)-optimal
270480.eg2 270480eg2 \([0, -1, 0, 24842200, 511295979552]\) \(14073614784514581404/945607964406328125\) \(-113919827358146659920000000\) \([2]\) \(82575360\) \(3.6794\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480.eg have rank \(1\).

Complex multiplication

The elliptic curves in class 270480.eg do not have complex multiplication.

Modular form 270480.2.a.eg

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 2 q^{11} - q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content 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.