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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7938.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7938.f1 | 7938o1 | \([1, -1, 0, -1500, 22742]\) | \(-18435447/2\) | \(-40507614\) | \([]\) | \(4032\) | \(0.48976\) | \(\Gamma_0(N)\)-optimal |
7938.f2 | 7938o2 | \([1, -1, 0, 9840, -754048]\) | \(44217/128\) | \(-305003537887104\) | \([]\) | \(28224\) | \(1.4627\) |
Rank
sage: E.rank()
The elliptic curves in class 7938.f have rank \(1\).
Complex multiplication
The elliptic curves in class 7938.f do not have complex multiplication.Modular form 7938.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.