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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 154800.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154800.bq1 | 154800ed2 | \([0, 0, 0, -78075, 5790250]\) | \(30459021867/9245000\) | \(15975360000000000\) | \([2]\) | \(884736\) | \(1.8142\) | |
154800.bq2 | 154800ed1 | \([0, 0, 0, -30075, -1937750]\) | \(1740992427/68800\) | \(118886400000000\) | \([2]\) | \(442368\) | \(1.4676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154800.bq have rank \(2\).
Complex multiplication
The elliptic curves in class 154800.bq do not have complex multiplication.Modular form 154800.2.a.bq
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.