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Properties

Label 5415c
Number of curves $2$
Conductor $5415$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 5415c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.h2 5415c1 \([1, 1, 0, 6852, 13707]\) \(756058031/438615\) \(-20635029094815\) \([2]\) \(14400\) \(1.2443\) \(\Gamma_0(N)\)-optimal
5415.h1 5415c2 \([1, 1, 0, -27443, 75438]\) \(48587168449/28048275\) \(1319555807905275\) \([2]\) \(28800\) \(1.5909\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5415c have rank \(2\).

Complex multiplication

The elliptic curves in class 5415c do not have complex multiplication.

Modular form 5415.2.a.c

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