Show commands:
SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 92400.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.da1 | 92400bp2 | \([0, -1, 0, -52491208, -146361229088]\) | \(7997484869919944276/116700507\) | \(233401014000000000\) | \([2]\) | \(5713920\) | \(2.8845\) | |
| 92400.da2 | 92400bp1 | \([0, -1, 0, -3283708, -2281669088]\) | \(7831544736466064/29831377653\) | \(14915688826500000000\) | \([2]\) | \(2856960\) | \(2.5379\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.da have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.da do not have complex multiplication.Modular form 92400.2.a.da
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.
