Properties

Label 384366t
Number of curves $2$
Conductor $384366$
CM no
Rank $0$
Graph

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

Elliptic curves in class 384366t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384366.t2 384366t1 \([1, 0, 0, -2255, -14232711]\) \(-117649/8118144\) \(-87507222247829376\) \([]\) \(2966264\) \(1.9298\) \(\Gamma_0(N)\)-optimal
384366.t1 384366t2 \([1, 0, 0, -14382845, 21055187199]\) \(-30526075007211889/103499257854\) \(-1115640786799960443966\) \([]\) \(20763848\) \(2.9027\)  

Rank

sage: E.rank()
 

The elliptic curves in class 384366t have rank \(0\).

Complex multiplication

The elliptic curves in class 384366t do not have complex multiplication.

Modular form 384366.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.