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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 206310bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206310.u4 | 206310bv1 | \([1, 0, 1, 2114666, -44417368]\) | \(7064514799444439/4094064000000\) | \(-606068403862896000000\) | \([2]\) | \(8553600\) | \(2.6773\) | \(\Gamma_0(N)\)-optimal |
206310.u3 | 206310bv2 | \([1, 0, 1, -8465334, -357585368]\) | \(453198971846635561/261896250564000\) | \(38770044278008491396000\) | \([2]\) | \(17107200\) | \(3.0238\) | |
206310.u2 | 206310bv3 | \([1, 0, 1, -28236709, 62295164432]\) | \(-16818951115904497561/1592332281446400\) | \(-235722324867316029849600\) | \([2]\) | \(25660800\) | \(3.2266\) | |
206310.u1 | 206310bv4 | \([1, 0, 1, -461593509, 3817071822352]\) | \(73474353581350183614361/576510977802240\) | \(85344315117213864591360\) | \([2]\) | \(51321600\) | \(3.5731\) |
Rank
sage: E.rank()
The elliptic curves in class 206310bv have rank \(0\).
Complex multiplication
The elliptic curves in class 206310bv do not have complex multiplication.Modular form 206310.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.