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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 20230j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20230.h2 | 20230j1 | \([1, -1, 0, -8554, -1157772]\) | \(-14090073029577/110146355200\) | \(-541149043097600\) | \([2]\) | \(80640\) | \(1.5100\) | \(\Gamma_0(N)\)-optimal |
20230.h1 | 20230j2 | \([1, -1, 0, -226154, -41239692]\) | \(260369943483538377/723136637440\) | \(3552770299742720\) | \([2]\) | \(161280\) | \(1.8565\) |
Rank
sage: E.rank()
The elliptic curves in class 20230j have rank \(1\).
Complex multiplication
The elliptic curves in class 20230j do not have complex multiplication.Modular form 20230.2.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 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.