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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2704.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2704.k1 | 2704m2 | \([0, 1, 0, -870744, -318254572]\) | \(-1680914269/32768\) | \(-1423311812421484544\) | \([]\) | \(37440\) | \(2.2768\) | |
| 2704.k2 | 2704m1 | \([0, 1, 0, 8056, 855284]\) | \(1331/8\) | \(-347488235454464\) | \([]\) | \(7488\) | \(1.4720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2704.k have rank \(1\).
Complex multiplication
The elliptic curves in class 2704.k do not have complex multiplication.Modular form 2704.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
