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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 37440.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.cf1 | 37440bg4 | \([0, 0, 0, -688908, 208885232]\) | \(189208196468929/10860320250\) | \(2075439520088064000\) | \([2]\) | \(442368\) | \(2.2688\) | |
| 37440.cf2 | 37440bg2 | \([0, 0, 0, -118668, -15664912]\) | \(967068262369/4928040\) | \(941763109847040\) | \([2]\) | \(147456\) | \(1.7195\) | |
| 37440.cf3 | 37440bg1 | \([0, 0, 0, -3468, -504592]\) | \(-24137569/561600\) | \(-107323431321600\) | \([2]\) | \(73728\) | \(1.3730\) | \(\Gamma_0(N)\)-optimal |
| 37440.cf4 | 37440bg3 | \([0, 0, 0, 31092, 13333232]\) | \(17394111071/411937500\) | \(-78722482176000000\) | \([2]\) | \(221184\) | \(1.9223\) |
Rank
sage: E.rank()
The elliptic curves in class 37440.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 37440.cf do not have complex multiplication.Modular form 37440.2.a.cf
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
