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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 152460.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.f1 | 152460bx3 | \([0, 0, 0, -1123848, -37051047]\) | \(281370820608/161767375\) | \(90252309560419314000\) | \([2]\) | \(3732480\) | \(2.5187\) | |
152460.f2 | 152460bx1 | \([0, 0, 0, -804408, -277690523]\) | \(75216478666752/326095\) | \(249565183615440\) | \([2]\) | \(1244160\) | \(1.9694\) | \(\Gamma_0(N)\)-optimal |
152460.f3 | 152460bx2 | \([0, 0, 0, -791703, -286886402]\) | \(-4481782160112/310023175\) | \(-3796242964481721600\) | \([2]\) | \(2488320\) | \(2.3160\) | |
152460.f4 | 152460bx4 | \([0, 0, 0, 4479057, -295905258]\) | \(1113258734352/648484375\) | \(-5788777872679956000000\) | \([2]\) | \(7464960\) | \(2.8653\) |
Rank
sage: E.rank()
The elliptic curves in class 152460.f have rank \(1\).
Complex multiplication
The elliptic curves in class 152460.f do not have complex multiplication.Modular form 152460.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.