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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 6096.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6096.d1 | 6096f2 | \([0, -1, 0, -357777696, 2604880956672]\) | \(1236526859255318155975783969/38367061931916216\) | \(157151485673128820736\) | \([]\) | \(620928\) | \(3.3796\) | |
6096.d2 | 6096f1 | \([0, -1, 0, -1631136, -793721088]\) | \(117174888570509216929/1273887851544576\) | \(5217844639926583296\) | \([]\) | \(88704\) | \(2.4067\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6096.d have rank \(0\).
Complex multiplication
The elliptic curves in class 6096.d do not have complex multiplication.Modular form 6096.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.