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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 435344.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.j1 | 435344j2 | \([0, 1, 0, -1637328, -755502188]\) | \(24553362849625/1755162752\) | \(34700637666584035328\) | \([2]\) | \(12644352\) | \(2.4964\) | \(\Gamma_0(N)\)-optimal* |
435344.j2 | 435344j1 | \([0, 1, 0, 93232, -51510380]\) | \(4533086375/60669952\) | \(-1199481939325616128\) | \([2]\) | \(6322176\) | \(2.1498\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.j have rank \(0\).
Complex multiplication
The elliptic curves in class 435344.j do not have complex multiplication.Modular form 435344.2.a.j
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 LMFDB 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 LMFDB labels.