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SageMath
E = EllipticCurve("sw1")
E.isogeny_class()
Elliptic curves in class 176400.sw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.sw1 | 176400ic2 | \([0, 0, 0, -24876075, -49546435750]\) | \(-6329617441/279936\) | \(-75292301924130816000000\) | \([]\) | \(15805440\) | \(3.1546\) | |
176400.sw2 | 176400ic1 | \([0, 0, 0, -180075, 67828250]\) | \(-2401/6\) | \(-1613775332736000000\) | \([]\) | \(2257920\) | \(2.1816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.sw have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.sw do not have complex multiplication.Modular form 176400.2.a.sw
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.