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Properties

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

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 301530di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.di2 301530di1 \([1, 0, 0, -1136018295940, -466043982973996528]\) \(-1095248516670909925403006195052049/2085842527704615412039680\) \(-308779552902759871924395332075520\) \([2]\) \(3666432000\) \(5.4887\) \(\Gamma_0(N)\)-optimal
301530.di1 301530di2 \([1, 0, 0, -18176301042820, -29826781737333526000]\) \(4486144075680775880097697589357030929/16270828779444633600\) \(2408666603131871261255270400\) \([2]\) \(7332864000\) \(5.8352\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 301530.2.a.di

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