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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 98192.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98192.m1 | 98192k2 | \([0, 0, 0, -37461331, 88251666450]\) | \(30171143454741297/351424\) | \(67719379699892224\) | \([2]\) | \(3317760\) | \(2.7956\) | |
98192.m2 | 98192k1 | \([0, 0, 0, -2343251, 1376560146]\) | \(7384117376817/25137152\) | \(4843927395004055552\) | \([2]\) | \(1658880\) | \(2.4491\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98192.m have rank \(1\).
Complex multiplication
The elliptic curves in class 98192.m do not have complex multiplication.Modular form 98192.2.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.