Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 92736bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.bg4 | 92736bh1 | \([0, 0, 0, -345036, 127251056]\) | \(-23771111713777/22848457968\) | \(-4366408314695712768\) | \([2]\) | \(1474560\) | \(2.2729\) | \(\Gamma_0(N)\)-optimal |
92736.bg3 | 92736bh2 | \([0, 0, 0, -6439116, 6287147120]\) | \(154502321244119857/55101928644\) | \(10530142547208044544\) | \([2, 2]\) | \(2949120\) | \(2.6194\) | |
92736.bg2 | 92736bh3 | \([0, 0, 0, -7366476, 4357867376]\) | \(231331938231569617/90942310746882\) | \(17379346228045932920832\) | \([2]\) | \(5898240\) | \(2.9660\) | |
92736.bg1 | 92736bh4 | \([0, 0, 0, -103017036, 402449774960]\) | \(632678989847546725777/80515134\) | \(15386681720438784\) | \([2]\) | \(5898240\) | \(2.9660\) |
Rank
sage: E.rank()
The elliptic curves in class 92736bh have rank \(0\).
Complex multiplication
The elliptic curves in class 92736bh do not have complex multiplication.Modular form 92736.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.