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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 331200u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
331200.u2 | 331200u1 | \([0, 0, 0, -3675, -218000]\) | \(-7529536/23805\) | \(-17353845000000\) | \([2]\) | \(737280\) | \(1.2269\) | \(\Gamma_0(N)\)-optimal |
331200.u1 | 331200u2 | \([0, 0, 0, -81300, -8912000]\) | \(1273760704/1725\) | \(80481600000000\) | \([2]\) | \(1474560\) | \(1.5735\) |
Rank
sage: E.rank()
The elliptic curves in class 331200u have rank \(1\).
Complex multiplication
The elliptic curves in class 331200u do not have complex multiplication.Modular form 331200.2.a.u
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.