Properties

Label 212160p
Number of curves $2$
Conductor $212160$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 212160p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.gu1 212160p1 \([0, 1, 0, -1124065, -458394337]\) \(2396726313900986596/4154072495625\) \(272241295073280000\) \([2]\) \(2949120\) \(2.2393\) \(\Gamma_0(N)\)-optimal
212160.gu2 212160p2 \([0, 1, 0, -772545, -749945025]\) \(-389032340685029858/1627263833203125\) \(-213288725145600000000\) \([2]\) \(5898240\) \(2.5859\)  

Rank

sage: E.rank()
 

The elliptic curves in class 212160p have rank \(1\).

Complex multiplication

The elliptic curves in class 212160p do not have complex multiplication.

Modular form 212160.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 2 q^{11} + q^{13} + q^{15} - q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.