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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 259182.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.m1 | 259182m2 | \([1, -1, 0, -3384816, -1326631762]\) | \(8400610251/3370318\) | \(1720636074152835741594\) | \([]\) | \(15510528\) | \(2.7728\) | |
259182.m2 | 259182m1 | \([1, -1, 0, -2945586, -1945096884]\) | \(4035973447539/952\) | \(666695561944104\) | \([]\) | \(5170176\) | \(2.2235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.m have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.m do not have complex multiplication.Modular form 259182.2.a.m
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.