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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 92400.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.bh1 | 92400dv4 | \([0, -1, 0, -352408, -80404688]\) | \(75627935783569/396165\) | \(25354560000000\) | \([2]\) | \(589824\) | \(1.7680\) | |
| 92400.bh2 | 92400dv2 | \([0, -1, 0, -22408, -1204688]\) | \(19443408769/1334025\) | \(85377600000000\) | \([2, 2]\) | \(294912\) | \(1.4214\) | |
| 92400.bh3 | 92400dv1 | \([0, -1, 0, -4408, 91312]\) | \(148035889/31185\) | \(1995840000000\) | \([2]\) | \(147456\) | \(1.0749\) | \(\Gamma_0(N)\)-optimal |
| 92400.bh4 | 92400dv3 | \([0, -1, 0, 19592, -5236688]\) | \(12994449551/192163125\) | \(-12298440000000000\) | \([2]\) | \(589824\) | \(1.7680\) |
Rank
sage: E.rank()
The elliptic curves in class 92400.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.bh do not have complex multiplication.Modular form 92400.2.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 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.
