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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 18200.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18200.c1 | 18200r1 | \([0, 1, 0, -11908, 458688]\) | \(46689225424/3901625\) | \(15606500000000\) | \([2]\) | \(55296\) | \(1.2735\) | \(\Gamma_0(N)\)-optimal |
18200.c2 | 18200r2 | \([0, 1, 0, 12592, 2124688]\) | \(13799183324/129390625\) | \(-2070250000000000\) | \([2]\) | \(110592\) | \(1.6201\) |
Rank
sage: E.rank()
The elliptic curves in class 18200.c have rank \(1\).
Complex multiplication
The elliptic curves in class 18200.c do not have complex multiplication.Modular form 18200.2.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.