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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 414400u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414400.u2 | 414400u1 | \([0, 1, 0, -79833, -13088537]\) | \(-879217912000/642837223\) | \(-41141582272000000\) | \([2]\) | \(3981312\) | \(1.8875\) | \(\Gamma_0(N)\)-optimal* |
414400.u1 | 414400u2 | \([0, 1, 0, -1448833, -671577537]\) | \(656914788557000/161061481\) | \(82463478272000000\) | \([2]\) | \(7962624\) | \(2.2341\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414400u have rank \(0\).
Complex multiplication
The elliptic curves in class 414400u do not have complex multiplication.Modular form 414400.2.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.