Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 34496.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34496.r1 | 34496do2 | \([0, 1, 0, -735457, -243008865]\) | \(1426487591593/2156\) | \(66493151707136\) | \([2]\) | \(294912\) | \(1.9204\) | |
| 34496.r2 | 34496do1 | \([0, 1, 0, -45537, -3882593]\) | \(-338608873/13552\) | \(-417956953587712\) | \([2]\) | \(147456\) | \(1.5738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34496.r have rank \(0\).
Complex multiplication
The elliptic curves in class 34496.r do not have complex multiplication.Modular form 34496.2.a.r
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.
