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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 172480.fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
172480.fe1 | 172480dd2 | \([0, 1, 0, -250161, 65154095]\) | \(-18330740176/8857805\) | \(-836624107467653120\) | \([]\) | \(2322432\) | \(2.1446\) | |
172480.fe2 | 172480dd1 | \([0, 1, 0, 24239, -1086065]\) | \(16674224/15125\) | \(-1428563806208000\) | \([]\) | \(774144\) | \(1.5953\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 172480.fe have rank \(0\).
Complex multiplication
The elliptic curves in class 172480.fe do not have complex multiplication.Modular form 172480.2.a.fe
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.