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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 310464.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.d1 | 310464d1 | \([0, 0, 0, -14140812, -20467249040]\) | \(55635379958596/24057\) | \(135218827945377792\) | \([2]\) | \(15482880\) | \(2.6295\) | \(\Gamma_0(N)\)-optimal |
| 310464.d2 | 310464d2 | \([0, 0, 0, -14070252, -20681610320]\) | \(-27403349188178/578739249\) | \(-6505918687763907084288\) | \([2]\) | \(30965760\) | \(2.9761\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.d have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.d do not have complex multiplication.Modular form 310464.2.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.
