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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 33327.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33327.f1 | 33327i2 | \([1, -1, 1, -79070, 7997798]\) | \(6163717745375/466948881\) | \(4141716568607583\) | \([2]\) | \(135168\) | \(1.7417\) | |
33327.f2 | 33327i1 | \([1, -1, 1, 4765, 553250]\) | \(1349232625/15752961\) | \(-139724715559023\) | \([2]\) | \(67584\) | \(1.3952\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33327.f have rank \(1\).
Complex multiplication
The elliptic curves in class 33327.f do not have complex multiplication.Modular form 33327.2.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.