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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 97020.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.m1 | 97020bo2 | \([0, 0, 0, -227703, 41747902]\) | \(59466754384/121275\) | \(2662729299014400\) | \([2]\) | \(737280\) | \(1.8463\) | |
97020.m2 | 97020bo1 | \([0, 0, 0, -9408, 1101373]\) | \(-67108864/343035\) | \(-470732501075760\) | \([2]\) | \(368640\) | \(1.4998\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.m have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.m do not have complex multiplication.Modular form 97020.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.