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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 31824.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31824.d1 | 31824bg1 | \([0, 0, 0, -13491, 583794]\) | \(90942871473/3321188\) | \(9917014228992\) | \([2]\) | \(73728\) | \(1.2634\) | \(\Gamma_0(N)\)-optimal |
| 31824.d2 | 31824bg2 | \([0, 0, 0, 5229, 2077650]\) | \(5295319407/627576794\) | \(-1873934265655296\) | \([2]\) | \(147456\) | \(1.6099\) |
Rank
sage: E.rank()
The elliptic curves in class 31824.d have rank \(2\).
Complex multiplication
The elliptic curves in class 31824.d do not have complex multiplication.Modular form 31824.2.a.d
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.
