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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 187200.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.el1 | 187200dh2 | \([0, 0, 0, -16500, 808000]\) | \(10648000/117\) | \(5458752000000\) | \([2]\) | \(294912\) | \(1.2587\) | |
187200.el2 | 187200dh1 | \([0, 0, 0, -1875, -11000]\) | \(1000000/507\) | \(369603000000\) | \([2]\) | \(147456\) | \(0.91214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.el have rank \(0\).
Complex multiplication
The elliptic curves in class 187200.el do not have complex multiplication.Modular form 187200.2.a.el
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.