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Properties

Label 18515.m
Number of curves $2$
Conductor $18515$
CM no
Rank $1$
Graph

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

Elliptic curves in class 18515.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.m1 18515g2 \([0, 1, 1, -859801, -307150395]\) \(-897625882624/875\) \(-68522112120875\) \([]\) \(139104\) \(1.9487\)  
18515.m2 18515g1 \([0, 1, 1, -8111, -627164]\) \(-753664/1715\) \(-134303339756915\) \([3]\) \(46368\) \(1.3994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18515.m have rank \(1\).

Complex multiplication

The elliptic curves in class 18515.m do not have complex multiplication.

Modular form 18515.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - q^{5} + q^{7} - 2 q^{9} + 3 q^{11} - 2 q^{12} - q^{13} - q^{15} + 4 q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.