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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 97344er
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97344.cw1 | 97344er1 | \([0, 0, 0, -20280, -509704]\) | \(256000/117\) | \(421573652517888\) | \([2]\) | \(344064\) | \(1.5012\) | \(\Gamma_0(N)\)-optimal |
97344.cw2 | 97344er2 | \([0, 0, 0, 70980, -3831568]\) | \(686000/507\) | \(-29229106574573568\) | \([2]\) | \(688128\) | \(1.8478\) |
Rank
sage: E.rank()
The elliptic curves in class 97344er have rank \(1\).
Complex multiplication
The elliptic curves in class 97344er do not have complex multiplication.Modular form 97344.2.a.er
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.