Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4160.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4160.c1 | 4160i1 | \([0, 1, 0, -53825, -4823777]\) | \(65787589563409/10400000\) | \(2726297600000\) | \([2]\) | \(15360\) | \(1.3967\) | \(\Gamma_0(N)\)-optimal |
4160.c2 | 4160i2 | \([0, 1, 0, -48705, -5773025]\) | \(-48743122863889/26406250000\) | \(-6922240000000000\) | \([2]\) | \(30720\) | \(1.7432\) |
Rank
sage: E.rank()
The elliptic curves in class 4160.c have rank \(1\).
Complex multiplication
The elliptic curves in class 4160.c do not have complex multiplication.Modular form 4160.2.a.c
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.