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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 238260q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238260.q2 | 238260q1 | \([0, 1, 0, -1495021, 633372080]\) | \(490935337222144/53514685125\) | \(40282328130291522000\) | \([2]\) | \(8294400\) | \(2.4956\) | \(\Gamma_0(N)\)-optimal |
238260.q1 | 238260q2 | \([0, 1, 0, -5644716, -4482371916]\) | \(1651537757878864/235683421875\) | \(2838511160116236000000\) | \([2]\) | \(16588800\) | \(2.8422\) |
Rank
sage: E.rank()
The elliptic curves in class 238260q have rank \(1\).
Complex multiplication
The elliptic curves in class 238260q do not have complex multiplication.Modular form 238260.2.a.q
sage: E.q_eigenform(10)
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.