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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 28880.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28880.d1 | 28880z2 | \([0, 1, 0, -4661, -92765]\) | \(7575076864/1953125\) | \(2888000000000\) | \([]\) | \(54432\) | \(1.1002\) | |
28880.d2 | 28880z1 | \([0, 1, 0, -1621, 24579]\) | \(318767104/125\) | \(184832000\) | \([]\) | \(18144\) | \(0.55092\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28880.d have rank \(1\).
Complex multiplication
The elliptic curves in class 28880.d do not have complex multiplication.Modular form 28880.2.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.