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Properties

Label 301530j
Number of curves $2$
Conductor $301530$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 301530j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.j2 301530j1 \([1, 1, 0, -270536409753, -54212011798214043]\) \(-14792237218207024357021405874281/16096194317584664985600000\) \(-2382814435320394213910468198400000\) \([2]\) \(3832012800\) \(5.3200\) \(\Gamma_0(N)\)-optimal
301530.j1 301530j2 \([1, 1, 0, -4329712363673, -3467663185155719067]\) \(60636459217476013230932523486570601/71681949850635000000000\) \(10611501171392169439515000000000\) \([2]\) \(7664025600\) \(5.6666\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301530j have rank \(1\).

Complex multiplication

The elliptic curves in class 301530j do not have complex multiplication.

Modular form 301530.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + 4 q^{13} - 4 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.