Properties

Label 303646t
Number of curves $2$
Conductor $303646$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 303646t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303646.t2 303646t1 \([1, -1, 1, -10237572, -11603238873]\) \(801581275315909089/70810888830976\) \(10482552878973702897664\) \([]\) \(43464960\) \(2.9655\) \(\Gamma_0(N)\)-optimal
303646.t1 303646t2 \([1, -1, 1, -5084384412, 139543508251047]\) \(98191033604529537629349729/10906239337336\) \(1614514835949305651704\) \([]\) \(304254720\) \(3.9385\)  

Rank

sage: E.rank()
 

The elliptic curves in class 303646t have rank \(1\).

Complex multiplication

The elliptic curves in class 303646t do not have complex multiplication.

Modular form 303646.2.a.t

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.