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Properties

Label 339762m
Number of curves $2$
Conductor $339762$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 339762m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
339762.m2 339762m1 \([1, 0, 0, -104160156, 409155902352]\) \(124976563139916356014105311169/836805677420123692416\) \(836805677420123692416\) \([7]\) \(43750336\) \(3.1967\) \(\Gamma_0(N)\)-optimal
339762.m1 339762m2 \([1, 0, 0, -3106076766, -66605543437698]\) \(3314059238965717412166686272528609/1392335368399818889959574566\) \(1392335368399818889959574566\) \([]\) \(306252352\) \(4.1697\)  

Rank

sage: E.rank()
 

The elliptic curves in class 339762m have rank \(0\).

Complex multiplication

The elliptic curves in class 339762m do not have complex multiplication.

Modular form 339762.2.a.m

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