Show commands:
SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 162240.eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.eb1 | 162240hl2 | \([0, -1, 0, -372025, 76252825]\) | \(131096512/18225\) | \(791621636394700800\) | \([2]\) | \(3354624\) | \(2.1609\) | |
162240.eb2 | 162240hl1 | \([0, -1, 0, -97400, -10473750]\) | \(150568768/16875\) | \(11452859322840000\) | \([2]\) | \(1677312\) | \(1.8143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.eb do not have complex multiplication.Modular form 162240.2.a.eb
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.