Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 214245.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214245.j1 | 214245q2 | \([0, 0, 1, -85698, 9608888]\) | \(884736/5\) | \(393361704430245\) | \([]\) | \(855360\) | \(1.6424\) | |
214245.j2 | 214245q1 | \([0, 0, 1, -6348, -185547]\) | \(2359296/125\) | \(1498863376125\) | \([]\) | \(285120\) | \(1.0931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214245.j have rank \(2\).
Complex multiplication
The elliptic curves in class 214245.j do not have complex multiplication.Modular form 214245.2.a.j
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.