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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 20328a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20328.e2 | 20328a1 | \([0, -1, 0, -1008, 179676]\) | \(-62500/7623\) | \(-13828720131072\) | \([2]\) | \(46080\) | \(1.2009\) | \(\Gamma_0(N)\)-optimal |
20328.e1 | 20328a2 | \([0, -1, 0, -54248, 4843500]\) | \(4866277250/43659\) | \(158401703319552\) | \([2]\) | \(92160\) | \(1.5475\) |
Rank
sage: E.rank()
The elliptic curves in class 20328a have rank \(0\).
Complex multiplication
The elliptic curves in class 20328a do not have complex multiplication.Modular form 20328.2.a.a
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.