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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 11830.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11830.c1 | 11830d2 | \([1, 0, 1, -950629, -332868144]\) | \(19683218700810001/1478750000000\) | \(7137643808750000000\) | \([2]\) | \(376320\) | \(2.3630\) | |
11830.c2 | 11830d1 | \([1, 0, 1, -193509, 26612432]\) | \(166021325905681/32614400000\) | \(157423479449600000\) | \([2]\) | \(188160\) | \(2.0164\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11830.c have rank \(0\).
Complex multiplication
The elliptic curves in class 11830.c do not have complex multiplication.Modular form 11830.2.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.