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Properties

Label 95370k
Number of curves $2$
Conductor $95370$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 95370k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95370.c2 95370k1 \([1, 1, 0, -7448574018, 247430010120372]\) \(385392122382860622756377/4657435200\) \(552315350290380494400\) \([2]\) \(87736320\) \(3.9981\) \(\Gamma_0(N)\)-optimal
95370.c1 95370k2 \([1, 1, 0, -7448770538, 247416300845868]\) \(385422627251821912561817/42366606723045000\) \(5024165925669430343773365000\) \([2]\) \(175472640\) \(4.3447\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95370k have rank \(2\).

Complex multiplication

The elliptic curves in class 95370k do not have complex multiplication.

Modular form 95370.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - 4 q^{13} + 4 q^{14} + q^{15} + q^{16} - q^{18} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.