Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 57960.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.i1 | 57960bl4 | \([0, 0, 0, -25535523, 49491158222]\) | \(2466780454987534385284/10072750481768625\) | \(7519267943638351488000\) | \([2]\) | \(4423680\) | \(3.0534\) | |
| 57960.i2 | 57960bl2 | \([0, 0, 0, -2383023, -69083278]\) | \(8019382352783901136/4629798816890625\) | \(864031574403396000000\) | \([2, 2]\) | \(2211840\) | \(2.7069\) | |
| 57960.i3 | 57960bl1 | \([0, 0, 0, -1679898, -835911403]\) | \(44949507773962418176/132895751953125\) | \(1550096050781250000\) | \([2]\) | \(1105920\) | \(2.3603\) | \(\Gamma_0(N)\)-optimal |
| 57960.i4 | 57960bl3 | \([0, 0, 0, 9519477, -552324778]\) | \(127801365439147434716/74135664409456125\) | \(-55341976939001359488000\) | \([2]\) | \(4423680\) | \(3.0534\) |
Rank
sage: E.rank()
The elliptic curves in class 57960.i have rank \(1\).
Complex multiplication
The elliptic curves in class 57960.i do not have complex multiplication.Modular form 57960.2.a.i
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.
