Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 37030g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37030.i2 | 37030g1 | \([1, -1, 0, -52424, -4606932]\) | \(1309589935642143/437500\) | \(5323062500\) | \([2]\) | \(82944\) | \(1.2242\) | \(\Gamma_0(N)\)-optimal |
37030.i1 | 37030g2 | \([1, -1, 0, -52654, -4564290]\) | \(1326902312327103/23925781250\) | \(291104980468750\) | \([2]\) | \(165888\) | \(1.5708\) |
Rank
sage: E.rank()
The elliptic curves in class 37030g have rank \(1\).
Complex multiplication
The elliptic curves in class 37030g do not have complex multiplication.Modular form 37030.2.a.g
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.