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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 75456u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75456.h2 | 75456u1 | \([0, 0, 0, -22764, -1320784]\) | \(6826561273/7074\) | \(1351862452224\) | \([]\) | \(233472\) | \(1.2455\) | \(\Gamma_0(N)\)-optimal |
75456.h1 | 75456u2 | \([0, 0, 0, -83244, 7847984]\) | \(333822098953/53954184\) | \(10310805130051584\) | \([]\) | \(700416\) | \(1.7948\) |
Rank
sage: E.rank()
The elliptic curves in class 75456u have rank \(0\).
Complex multiplication
The elliptic curves in class 75456u do not have complex multiplication.Modular form 75456.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.