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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 388416.fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388416.fm1 | 388416fm2 | \([0, 1, 0, -7056609, -7216415073]\) | \(6141556990297/1019592\) | \(6451487637988442112\) | \([2]\) | \(10616832\) | \(2.6172\) | |
388416.fm2 | 388416fm1 | \([0, 1, 0, -398049, -135702369]\) | \(-1102302937/616896\) | \(-3903421091892166656\) | \([2]\) | \(5308416\) | \(2.2707\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388416.fm have rank \(0\).
Complex multiplication
The elliptic curves in class 388416.fm do not have complex multiplication.Modular form 388416.2.a.fm
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.