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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 158400dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.ge1 | 158400dn1 | \([0, 0, 0, -14700, 1874000]\) | \(-117649/440\) | \(-1313832960000000\) | \([]\) | \(552960\) | \(1.5866\) | \(\Gamma_0(N)\)-optimal |
158400.ge2 | 158400dn2 | \([0, 0, 0, 129300, -44494000]\) | \(80062991/332750\) | \(-993586176000000000\) | \([]\) | \(1658880\) | \(2.1359\) |
Rank
sage: E.rank()
The elliptic curves in class 158400dn have rank \(2\).
Complex multiplication
The elliptic curves in class 158400dn do not have complex multiplication.Modular form 158400.2.a.dn
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.