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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 98736.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.x1 | 98736bs2 | \([0, -1, 0, -227168, -41598720]\) | \(-2615903802147625/408\) | \(-202211328\) | \([]\) | \(300672\) | \(1.4402\) | |
98736.x2 | 98736bs1 | \([0, -1, 0, -2768, -57792]\) | \(-4734057625/265302\) | \(-131487916032\) | \([]\) | \(100224\) | \(0.89091\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.x have rank \(1\).
Complex multiplication
The elliptic curves in class 98736.x do not have complex multiplication.Modular form 98736.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.