Show commands:
SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 135240.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135240.du1 | 135240j2 | \([0, 1, 0, -63520, 5127968]\) | \(117636968738/20539575\) | \(4948911020390400\) | \([2]\) | \(884736\) | \(1.7314\) | |
135240.du2 | 135240j1 | \([0, 1, 0, -18440, -894720]\) | \(5756278756/499905\) | \(60224843105280\) | \([2]\) | \(442368\) | \(1.3848\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 135240.du have rank \(0\).
Complex multiplication
The elliptic curves in class 135240.du do not have complex multiplication.Modular form 135240.2.a.du
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.