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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2254a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2254.a2 | 2254a1 | \([1, 0, 1, 1689, -125590]\) | \(4533086375/60669952\) | \(-7137759182848\) | \([2]\) | \(5376\) | \(1.1471\) | \(\Gamma_0(N)\)-optimal |
2254.a1 | 2254a2 | \([1, 0, 1, -29671, -1844118]\) | \(24553362849625/1755162752\) | \(206493142610048\) | \([2]\) | \(10752\) | \(1.4937\) |
Rank
sage: E.rank()
The elliptic curves in class 2254a have rank \(0\).
Complex multiplication
The elliptic curves in class 2254a do not have complex multiplication.Modular form 2254.2.a.a
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.