Show commands:
SageMath
E = EllipticCurve("if1")
E.isogeny_class()
Elliptic curves in class 148800.if
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148800.if1 | 148800bv4 | \([0, 1, 0, -10605633, -13297219137]\) | \(32208729120020809/658986840\) | \(2699210096640000000\) | \([2]\) | \(5308416\) | \(2.6562\) | |
148800.if2 | 148800bv2 | \([0, 1, 0, -685633, -192899137]\) | \(8702409880009/1120910400\) | \(4591248998400000000\) | \([2, 2]\) | \(2654208\) | \(2.3096\) | |
148800.if3 | 148800bv1 | \([0, 1, 0, -173633, 24700863]\) | \(141339344329/17141760\) | \(70212648960000000\) | \([2]\) | \(1327104\) | \(1.9630\) | \(\Gamma_0(N)\)-optimal |
148800.if4 | 148800bv3 | \([0, 1, 0, 1042367, -1006787137]\) | \(30579142915511/124675335000\) | \(-510670172160000000000\) | \([2]\) | \(5308416\) | \(2.6562\) |
Rank
sage: E.rank()
The elliptic curves in class 148800.if have rank \(0\).
Complex multiplication
The elliptic curves in class 148800.if do not have complex multiplication.Modular form 148800.2.a.if
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.