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Properties

Label 30015e
Number of curves $2$
Conductor $30015$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 30015e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30015.m1 30015e1 \([1, -1, 0, -360, -2525]\) \(7088952961/50025\) \(36468225\) \([2]\) \(16384\) \(0.28367\) \(\Gamma_0(N)\)-optimal
30015.m2 30015e2 \([1, -1, 0, -135, -5810]\) \(-374805361/20020005\) \(-14594583645\) \([2]\) \(32768\) \(0.63024\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30015e have rank \(1\).

Complex multiplication

The elliptic curves in class 30015e do not have complex multiplication.

Modular form 30015.2.a.e

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