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Properties

Label 30345.u
Number of curves $2$
Conductor $30345$
CM no
Rank $1$
Graph

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

Elliptic curves in class 30345.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30345.u1 30345a2 \([1, 1, 0, -361520943, -2343460232862]\) \(216486375407331255135001/27004994294227023375\) \(651834913121511078378675375\) \([2]\) \(11612160\) \(3.8748\)  
30345.u2 30345a1 \([1, 1, 0, 33505932, -189536694237]\) \(172343644217341694999/742780064187984375\) \(-17928905051161901822484375\) \([2]\) \(5806080\) \(3.5282\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30345.u have rank \(1\).

Complex multiplication

The elliptic curves in class 30345.u do not have complex multiplication.

Modular form 30345.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.