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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 60840u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60840.bu2 | 60840u1 | \([0, 0, 0, -507, -2851706]\) | \(-4/975\) | \(-3513113770982400\) | \([2]\) | \(258048\) | \(1.6618\) | \(\Gamma_0(N)\)-optimal |
60840.bu1 | 60840u2 | \([0, 0, 0, -304707, -63752546]\) | \(434163602/7605\) | \(54804574827325440\) | \([2]\) | \(516096\) | \(2.0084\) |
Rank
sage: E.rank()
The elliptic curves in class 60840u have rank \(1\).
Complex multiplication
The elliptic curves in class 60840u do not have complex multiplication.Modular form 60840.2.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.