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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 123840.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.l1 | 123840ci4 | \([0, 0, 0, -330348, -73081168]\) | \(41725476313778/17415\) | \(1664029163520\) | \([2]\) | \(786432\) | \(1.6896\) | |
| 123840.l2 | 123840ci2 | \([0, 0, 0, -20748, -1130128]\) | \(20674973956/416025\) | \(19875903897600\) | \([2, 2]\) | \(393216\) | \(1.3430\) | |
| 123840.l3 | 123840ci1 | \([0, 0, 0, -2748, 29072]\) | \(192143824/80625\) | \(962979840000\) | \([2]\) | \(196608\) | \(0.99641\) | \(\Gamma_0(N)\)-optimal |
| 123840.l4 | 123840ci3 | \([0, 0, 0, 852, -3367888]\) | \(715822/51282015\) | \(-4900072840888320\) | \([2]\) | \(786432\) | \(1.6896\) |
Rank
sage: E.rank()
The elliptic curves in class 123840.l have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.l do not have complex multiplication.Modular form 123840.2.a.l
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.
