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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 64400.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.o1 | 64400ce2 | \([0, -1, 0, -10421306208, 411961124230912]\) | \(-78229436189152112196207745/549794097750525813248\) | \(-879670556400841301196800000000\) | \([]\) | \(78382080\) | \(4.5790\) | |
| 64400.o2 | 64400ce1 | \([0, -1, 0, 366533792, 3011671430912]\) | \(3403656999841015798655/4418852112356605952\) | \(-7070163379770569523200000000\) | \([]\) | \(26127360\) | \(4.0297\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.o have rank \(0\).
Complex multiplication
The elliptic curves in class 64400.o do not have complex multiplication.Modular form 64400.2.a.o
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.
