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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4554u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4554.z1 | 4554u1 | \([1, -1, 1, -35, 155]\) | \(-170953875/244904\) | \(-6612408\) | \([3]\) | \(864\) | \(0.00081619\) | \(\Gamma_0(N)\)-optimal |
4554.z2 | 4554u2 | \([1, -1, 1, 295, -2969]\) | \(144703125/267674\) | \(-5268627342\) | \([]\) | \(2592\) | \(0.55012\) |
Rank
sage: E.rank()
The elliptic curves in class 4554u have rank \(1\).
Complex multiplication
The elliptic curves in class 4554u do not have complex multiplication.Modular form 4554.2.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.