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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 441090.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
441090.m1 | 441090m1 | \([1, -1, 0, -758250, -253437404]\) | \(13701674594089/31758480\) | \(111749953358843280\) | \([2]\) | \(7569408\) | \(2.1520\) | \(\Gamma_0(N)\)-optimal |
441090.m2 | 441090m2 | \([1, -1, 0, -484470, -439115000]\) | \(-3573857582569/21617820900\) | \(-76067572418290404900\) | \([2]\) | \(15138816\) | \(2.4985\) |
Rank
sage: E.rank()
The elliptic curves in class 441090.m have rank \(1\).
Complex multiplication
The elliptic curves in class 441090.m do not have complex multiplication.Modular form 441090.2.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.