Properties

Label 30015.d
Number of curves $2$
Conductor $30015$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 30015.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30015.d1 30015m1 \([1, -1, 1, -3362, -74176]\) \(5763259856089/450225\) \(328214025\) \([2]\) \(13824\) \(0.68134\) \(\Gamma_0(N)\)-optimal
30015.d2 30015m2 \([1, -1, 1, -3137, -84706]\) \(-4681768588489/1621620405\) \(-1182161275245\) \([2]\) \(27648\) \(1.0279\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30015.d have rank \(0\).

Complex multiplication

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

Modular form 30015.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 3 q^{8} - q^{10} - 2 q^{11} + 2 q^{13} - q^{16} + 4 q^{17} + O(q^{20})\) 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.