Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 45486k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45486.r1 | 45486k1 | \([1, -1, 0, -297351, 61905865]\) | \(84778086457/904932\) | \(31035952601932068\) | \([2]\) | \(460800\) | \(1.9803\) | \(\Gamma_0(N)\)-optimal |
| 45486.r2 | 45486k2 | \([1, -1, 0, -69921, 154105987]\) | \(-1102302937/298433646\) | \(-10235213797365739854\) | \([2]\) | \(921600\) | \(2.3269\) |
Rank
sage: E.rank()
The elliptic curves in class 45486k have rank \(1\).
Complex multiplication
The elliptic curves in class 45486k do not have complex multiplication.Modular form 45486.2.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 Cremona 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 Cremona labels.
