Properties

Label 215475u
Number of curves $2$
Conductor $215475$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 215475u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.m2 215475u1 \([1, 1, 1, -139513, -19075594]\) \(3981876625/232713\) \(17550956294015625\) \([2]\) \(1548288\) \(1.8705\) \(\Gamma_0(N)\)-optimal
215475.m1 215475u2 \([1, 1, 1, -414138, 78690906]\) \(104154702625/24649677\) \(1859051293604578125\) \([2]\) \(3096576\) \(2.2171\)  

Rank

sage: E.rank()
 

The elliptic curves in class 215475u have rank \(1\).

Complex multiplication

The elliptic curves in class 215475u do not have complex multiplication.

Modular form 215475.2.a.u

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