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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 92400.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.b1 | 92400dn4 | \([0, -1, 0, -1196295408, -15867782618688]\) | \(2958414657792917260183849/12401051653985258880\) | \(793667305855056568320000000\) | \([2]\) | \(57802752\) | \(4.0162\) | |
| 92400.b2 | 92400dn2 | \([0, -1, 0, -112135408, 26002981312]\) | \(2436531580079063806249/1405478914998681600\) | \(89950650559915622400000000\) | \([2, 2]\) | \(28901376\) | \(3.6696\) | |
| 92400.b3 | 92400dn1 | \([0, -1, 0, -79367408, 271500837312]\) | \(863913648706111516969/2486234429521920\) | \(159119003489402880000000\) | \([2]\) | \(14450688\) | \(3.3231\) | \(\Gamma_0(N)\)-optimal |
| 92400.b4 | 92400dn3 | \([0, -1, 0, 447736592, 207401509312]\) | \(155099895405729262880471/90047655797243760000\) | \(-5763049971023600640000000000\) | \([2]\) | \(57802752\) | \(4.0162\) |
Rank
sage: E.rank()
The elliptic curves in class 92400.b have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.b do not have complex multiplication.Modular form 92400.2.a.b
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.
