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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 279174i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279174.i1 | 279174i1 | \([1, 1, 0, -41545, -3276683]\) | \(1614171115147625/1877904\) | \(9226142352\) | \([2]\) | \(589824\) | \(1.1955\) | \(\Gamma_0(N)\)-optimal |
279174.i2 | 279174i2 | \([1, 1, 0, -41205, -3332511]\) | \(-1574864421763625/55101928644\) | \(-270715775427972\) | \([2]\) | \(1179648\) | \(1.5421\) |
Rank
sage: E.rank()
The elliptic curves in class 279174i have rank \(1\).
Complex multiplication
The elliptic curves in class 279174i do not have complex multiplication.Modular form 279174.2.a.i
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.