Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 59248.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59248.i1 | 59248p2 | \([0, 1, 0, -21336, -1192268]\) | \(3543122/49\) | \(14855697532928\) | \([2]\) | \(180224\) | \(1.3331\) | |
59248.i2 | 59248p1 | \([0, 1, 0, -176, -49628]\) | \(-4/7\) | \(-1061121252352\) | \([2]\) | \(90112\) | \(0.98650\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59248.i have rank \(1\).
Complex multiplication
The elliptic curves in class 59248.i do not have complex multiplication.Modular form 59248.2.a.i
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.