Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 27930c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27930.i2 | 27930c1 | \([1, 1, 0, 345012, 66135168]\) | \(13241287869457332257/13147628906250000\) | \(-4509636714843750000\) | \([2]\) | \(506880\) | \(2.2663\) | \(\Gamma_0(N)\)-optimal |
27930.i1 | 27930c2 | \([1, 1, 0, -1842488, 602947668]\) | \(2016712380478747667743/708035157428062500\) | \(242856058997825437500\) | \([2]\) | \(1013760\) | \(2.6129\) |
Rank
sage: E.rank()
The elliptic curves in class 27930c have rank \(0\).
Complex multiplication
The elliptic curves in class 27930c do not have complex multiplication.Modular form 27930.2.a.c
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.