Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 244398.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244398.bl1 | 244398bl2 | \([1, 0, 0, -16126949526408, 24927368290379869248]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-22734553042824775713792\) | \([]\) | \(4742115840\) | \(5.6822\) | |
244398.bl2 | 244398bl1 | \([1, 0, 0, -199096393608, 34194536777001024]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-31941923101519397077393235509248\) | \([]\) | \(1580705280\) | \(5.1329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244398.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 244398.bl do not have complex multiplication.Modular form 244398.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.