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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 290145.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.m1 | 290145m2 | \([0, -1, 1, -2000790581, -34393931522713]\) | \(1489157481162281146384384/2616603057861328125\) | \(1556416520615830352783203125\) | \([]\) | \(163296000\) | \(4.1109\) | |
290145.m2 | 290145m1 | \([0, -1, 1, -104301941, 365368613786]\) | \(210966209738334797824/25153051046653125\) | \(14961621356852737747528125\) | \([]\) | \(54432000\) | \(3.5616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 290145.m have rank \(1\).
Complex multiplication
The elliptic curves in class 290145.m do not have complex multiplication.Modular form 290145.2.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.