Show commands:
SageMath
E = EllipticCurve("hw1")
E.isogeny_class()
Elliptic curves in class 346560.hw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.hw1 | 346560hw2 | \([0, 1, 0, -69261, 6992829]\) | \(1590409933520896/45\) | \(1039680\) | \([]\) | \(559872\) | \(1.1151\) | |
| 346560.hw2 | 346560hw1 | \([0, 1, 0, -861, 9189]\) | \(3058794496/91125\) | \(2105352000\) | \([]\) | \(186624\) | \(0.56582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.hw have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.hw do not have complex multiplication.Modular form 346560.2.a.hw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
