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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 374850.fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.fh1 | 374850fh2 | \([1, -1, 0, -181021542, 937479772116]\) | \(13217291350697580147/90312500000\) | \(4482495834960937500000\) | \([2]\) | \(55296000\) | \(3.3354\) | |
374850.fh2 | 374850fh1 | \([1, -1, 0, -11089542, 15258808116]\) | \(-3038732943445107/267267200000\) | \(-13265318874150000000000\) | \([2]\) | \(27648000\) | \(2.9888\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374850.fh have rank \(0\).
Complex multiplication
The elliptic curves in class 374850.fh do not have complex multiplication.Modular form 374850.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.