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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 259920.er
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.er1 | 259920er2 | \([0, 0, 0, -189534747, 1004340419786]\) | \(781484460931/900\) | \(867186272308436582400\) | \([2]\) | \(28016640\) | \(3.3017\) | |
259920.er2 | 259920er1 | \([0, 0, 0, -11749467, 15960934154]\) | \(-186169411/6480\) | \(-6243741160620743393280\) | \([2]\) | \(14008320\) | \(2.9551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.er have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.er do not have complex multiplication.Modular form 259920.2.a.er
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.