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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 211600.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
211600.u1 | 211600s2 | \([0, 1, 0, -24232608, 45914348788]\) | \(-313994137/64\) | \(-320761795710976000000\) | \([]\) | \(14307840\) | \(2.9323\) | |
211600.u2 | 211600s1 | \([0, 1, 0, 101392, 215096788]\) | \(23/4\) | \(-20047612231936000000\) | \([]\) | \(4769280\) | \(2.3830\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 211600.u have rank \(1\).
Complex multiplication
The elliptic curves in class 211600.u do not have complex multiplication.Modular form 211600.2.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.