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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 20160c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.l2 | 20160c1 | \([0, 0, 0, 72, -152]\) | \(1492992/1225\) | \(-33868800\) | \([2]\) | \(4096\) | \(0.13261\) | \(\Gamma_0(N)\)-optimal |
20160.l1 | 20160c2 | \([0, 0, 0, -348, -1328]\) | \(10536048/4375\) | \(1935360000\) | \([2]\) | \(8192\) | \(0.47919\) |
Rank
sage: E.rank()
The elliptic curves in class 20160c have rank \(1\).
Complex multiplication
The elliptic curves in class 20160c do not have complex multiplication.Modular form 20160.2.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 Cremona 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 Cremona labels.