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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9408.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.d1 | 9408d2 | \([0, -1, 0, -45537, -3744159]\) | \(-16591834777/98304\) | \(-61873298866176\) | \([]\) | \(34560\) | \(1.4866\) | |
9408.d2 | 9408d1 | \([0, -1, 0, 1503, -27999]\) | \(596183/864\) | \(-543808290816\) | \([]\) | \(11520\) | \(0.93733\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.d have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.d do not have complex multiplication.Modular form 9408.2.a.d
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.