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Properties

Label 220218.t
Number of curves $2$
Conductor $220218$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 220218.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
220218.t1 220218p2 \([1, 1, 1, -6462359640, -199958852329887]\) \(1236526859255318155975783969/38367061931916216\) \(926087604708900965918904\) \([]\) \(130394880\) \(4.1031\)  
220218.t2 220218p1 \([1, 1, 1, -29462400, 60959957793]\) \(117174888570509216929/1273887851544576\) \(30748555914918959775744\) \([]\) \(18627840\) \(3.1301\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 220218.t have rank \(1\).

Complex multiplication

The elliptic curves in class 220218.t do not have complex multiplication.

Modular form 220218.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} - q^{14} - q^{15} + q^{16} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.