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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 370881ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
370881.ba2 | 370881ba1 | \([1, -1, 0, -43215363, 109212303640]\) | \(510082399/783\) | \(13701232558229008349529\) | \([2]\) | \(27095040\) | \(3.1471\) | \(\Gamma_0(N)\)-optimal |
370881.ba1 | 370881ba2 | \([1, -1, 0, -56196198, 38199347689]\) | \(1121622319/613089\) | \(10728065093093313537681207\) | \([2]\) | \(54190080\) | \(3.4937\) |
Rank
sage: E.rank()
The elliptic curves in class 370881ba have rank \(1\).
Complex multiplication
The elliptic curves in class 370881ba do not have complex multiplication.Modular form 370881.2.a.ba
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.