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SageMath
E = EllipticCurve("iy1")
E.isogeny_class()
Elliptic curves in class 162624iy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162624.ds2 | 162624iy1 | \([0, -1, 0, -29, -9]\) | \(360448/189\) | \(1463616\) | \([]\) | \(27648\) | \(-0.12525\) | \(\Gamma_0(N)\)-optimal |
162624.ds1 | 162624iy2 | \([0, -1, 0, -1349, 19527]\) | \(35084566528/1029\) | \(7968576\) | \([]\) | \(82944\) | \(0.42406\) |
Rank
sage: E.rank()
The elliptic curves in class 162624iy have rank \(0\).
Complex multiplication
The elliptic curves in class 162624iy do not have complex multiplication.Modular form 162624.2.a.iy
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.