Show commands:
SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 130050ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130050.z1 | 130050ev1 | \([1, -1, 0, -163917, -16175759]\) | \(1771561/612\) | \(168264502097062500\) | \([2]\) | \(1474560\) | \(2.0071\) | \(\Gamma_0(N)\)-optimal |
130050.z2 | 130050ev2 | \([1, -1, 0, 486333, -113063009]\) | \(46268279/46818\) | \(-12872234410425281250\) | \([2]\) | \(2949120\) | \(2.3537\) |
Rank
sage: E.rank()
The elliptic curves in class 130050ev have rank \(0\).
Complex multiplication
The elliptic curves in class 130050ev do not have complex multiplication.Modular form 130050.2.a.ev
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.