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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 348480eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348480.eo2 | 348480eo1 | \([0, 0, 0, 15972, -18037712]\) | \(16/5\) | \(-140815881563258880\) | \([2]\) | \(2433024\) | \(1.9697\) | \(\Gamma_0(N)\)-optimal |
348480.eo1 | 348480eo2 | \([0, 0, 0, -942348, -342716528]\) | \(821516/25\) | \(2816317631265177600\) | \([2]\) | \(4866048\) | \(2.3162\) |
Rank
sage: E.rank()
The elliptic curves in class 348480eo have rank \(1\).
Complex multiplication
The elliptic curves in class 348480eo do not have complex multiplication.Modular form 348480.2.a.eo
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.