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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 43350.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43350.c1 | 43350w2 | \([1, 1, 0, -52403075, 145988392125]\) | \(337575153545189/2448\) | \(115407751781250000\) | \([2]\) | \(3686400\) | \(2.8702\) | |
43350.c2 | 43350w1 | \([1, 1, 0, -3273075, 2283142125]\) | \(-82256120549/221952\) | \(-10463636161500000000\) | \([2]\) | \(1843200\) | \(2.5236\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43350.c have rank \(0\).
Complex multiplication
The elliptic curves in class 43350.c do not have complex multiplication.Modular form 43350.2.a.c
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.