Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 270480.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.j1 | 270480j1 | \([0, -1, 0, -93599816, 348562527216]\) | \(188191720927962271801/9422571110400\) | \(4540645656852273561600\) | \([2]\) | \(31850496\) | \(3.2265\) | \(\Gamma_0(N)\)-optimal |
270480.j2 | 270480j2 | \([0, -1, 0, -88582216, 387587412976]\) | \(-159520003524722950201/42335913815758080\) | \(-20401266378793461161656320\) | \([2]\) | \(63700992\) | \(3.5731\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.j have rank \(2\).
Complex multiplication
The elliptic curves in class 270480.j do not have complex multiplication.Modular form 270480.2.a.j
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.