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Properties

Label 308898z
Number of curves $2$
Conductor $308898$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 308898z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308898.z2 308898z1 \([1, -1, 0, -6103953, 5800827987]\) \(6826561273/7074\) \(26062757173747325826\) \([]\) \(20866560\) \(2.6433\) \(\Gamma_0(N)\)-optimal
308898.z1 308898z2 \([1, -1, 0, -22321098, -34453369332]\) \(333822098953/53954184\) \(198783544826079048222216\) \([]\) \(62599680\) \(3.1926\)  

Rank

sage: E.rank()
 

The elliptic curves in class 308898z have rank \(1\).

Complex multiplication

The elliptic curves in class 308898z do not have complex multiplication.

Modular form 308898.2.a.z

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.