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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 271040.fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271040.fh1 | 271040fh1 | \([0, 1, 0, -27265, -1745537]\) | \(-584043889/1400\) | \(-5373270425600\) | \([]\) | \(663552\) | \(1.3221\) | \(\Gamma_0(N)\)-optimal |
271040.fh2 | 271040fh2 | \([0, 1, 0, 50175, -8730625]\) | \(3639707951/10718750\) | \(-41139101696000000\) | \([]\) | \(1990656\) | \(1.8714\) |
Rank
sage: E.rank()
The elliptic curves in class 271040.fh have rank \(0\).
Complex multiplication
The elliptic curves in class 271040.fh do not have complex multiplication.Modular form 271040.2.a.fh
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.