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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 22050.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.m1 | 22050cp2 | \([1, -1, 0, -501867, -192162209]\) | \(-417267265/235298\) | \(-7883045601194531250\) | \([]\) | \(518400\) | \(2.3291\) | |
22050.m2 | 22050cp1 | \([1, -1, 0, 49383, 3531541]\) | \(397535/392\) | \(-13132937278125000\) | \([]\) | \(172800\) | \(1.7798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22050.m have rank \(0\).
Complex multiplication
The elliptic curves in class 22050.m do not have complex multiplication.Modular form 22050.2.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.