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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 388080ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.ds2 | 388080ds1 | \([0, 0, 0, -9408, 20354992]\) | \(-262144/509355\) | \(-178935408893767680\) | \([]\) | \(3981312\) | \(1.9895\) | \(\Gamma_0(N)\)-optimal |
388080.ds1 | 388080ds2 | \([0, 0, 0, -5936448, 5567471728]\) | \(-65860951343104/3493875\) | \(-1227391410212352000\) | \([]\) | \(11943936\) | \(2.5388\) |
Rank
sage: E.rank()
The elliptic curves in class 388080ds have rank \(0\).
Complex multiplication
The elliptic curves in class 388080ds do not have complex multiplication.Modular form 388080.2.a.ds
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 Cremona 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 Cremona labels.