Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 88935.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.x1 | 88935ck1 | \([1, 0, 0, -1147385, -470981400]\) | \(2336752783/12375\) | \(884674845085271625\) | \([2]\) | \(1612800\) | \(2.2883\) | \(\Gamma_0(N)\)-optimal |
88935.x2 | 88935ck2 | \([1, 0, 0, -524840, -979849683]\) | \(-223648543/5671875\) | \(-405475970664082828125\) | \([2]\) | \(3225600\) | \(2.6349\) |
Rank
sage: E.rank()
The elliptic curves in class 88935.x have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.x do not have complex multiplication.Modular form 88935.2.a.x
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.