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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 33635.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33635.f1 | 33635f2 | \([1, 1, 1, -178766, -29165432]\) | \(711882749089/33635\) | \(29851186310435\) | \([2]\) | \(153600\) | \(1.6596\) | |
33635.f2 | 33635f1 | \([1, 1, 1, -10591, -508412]\) | \(-148035889/37975\) | \(-33702952285975\) | \([2]\) | \(76800\) | \(1.3130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33635.f have rank \(1\).
Complex multiplication
The elliptic curves in class 33635.f do not have complex multiplication.Modular form 33635.2.a.f
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.