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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 68445.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68445.u1 | 68445o2 | \([0, 0, 1, -18252, -904615]\) | \(2359296/125\) | \(35627280580125\) | \([]\) | \(155520\) | \(1.3571\) | |
68445.u2 | 68445o1 | \([0, 0, 1, -3042, 64262]\) | \(884736/5\) | \(17593718805\) | \([]\) | \(51840\) | \(0.80784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68445.u have rank \(2\).
Complex multiplication
The elliptic curves in class 68445.u do not have complex multiplication.Modular form 68445.2.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 LMFDB 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 LMFDB labels.