Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 435120.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.l1 | 435120l2 | \([0, -1, 0, -6873736, 5815928560]\) | \(74533948968883321/12833853739560\) | \(6184509680048105226240\) | \([2]\) | \(24772608\) | \(2.9017\) | \(\Gamma_0(N)\)-optimal* |
435120.l2 | 435120l1 | \([0, -1, 0, 809464, 517593840]\) | \(121721586383879/310858430400\) | \(-149799663526418841600\) | \([2]\) | \(12386304\) | \(2.5551\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120.l have rank \(1\).
Complex multiplication
The elliptic curves in class 435120.l do not have complex multiplication.Modular form 435120.2.a.l
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.