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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 119952.fo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.fo1 | 119952w2 | \([0, 0, 0, -72219, -7469462]\) | \(81344187038/7803\) | \(3995887085568\) | \([2]\) | \(442368\) | \(1.4545\) | |
119952.fo2 | 119952w1 | \([0, 0, 0, -4179, -134750]\) | \(-31522396/12393\) | \(-3173204450304\) | \([2]\) | \(221184\) | \(1.1079\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.fo have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.fo do not have complex multiplication.Modular form 119952.2.a.fo
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.