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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 10800.dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10800.dd1 | 10800ca2 | \([0, 0, 0, -615, -5870]\) | \(16541040\) | \(1555200\) | \([]\) | \(2592\) | \(0.24892\) | |
10800.dd2 | 10800ca1 | \([0, 0, 0, -15, 10]\) | \(2160\) | \(172800\) | \([]\) | \(864\) | \(-0.30039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10800.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 10800.dd do not have complex multiplication.Modular form 10800.2.a.dd
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.