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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 15600.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15600.e1 | 15600bj2 | \([0, -1, 0, -341008, 76760512]\) | \(68523370149961/243360\) | \(15575040000000\) | \([2]\) | \(92160\) | \(1.7497\) | |
15600.e2 | 15600bj1 | \([0, -1, 0, -21008, 1240512]\) | \(-16022066761/998400\) | \(-63897600000000\) | \([2]\) | \(46080\) | \(1.4031\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.e have rank \(1\).
Complex multiplication
The elliptic curves in class 15600.e do not have complex multiplication.Modular form 15600.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.