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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 35728.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35728.c1 | 35728h2 | \([0, 1, 0, -13608, 606484]\) | \(136084473031250/15631\) | \(32012288\) | \([2]\) | \(31744\) | \(0.86318\) | |
35728.c2 | 35728h1 | \([0, 1, 0, -848, 9316]\) | \(-65936114500/712327\) | \(-729422848\) | \([2]\) | \(15872\) | \(0.51661\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35728.c have rank \(2\).
Complex multiplication
The elliptic curves in class 35728.c do not have complex multiplication.Modular form 35728.2.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.