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SageMath
E = EllipticCurve("if1")
E.isogeny_class()
Elliptic curves in class 139650.if
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139650.if1 | 139650bv3 | \([1, 0, 0, -1510968313, 22606184778617]\) | \(207530301091125281552569/805586668007040\) | \(1480882279755628890000000\) | \([2]\) | \(61931520\) | \(3.8511\) | |
| 139650.if2 | 139650bv4 | \([1, 0, 0, -286360313, -1440137941383]\) | \(1412712966892699019449/330160465517040000\) | \(606922634493972483750000000\) | \([2]\) | \(61931520\) | \(3.8511\) | |
| 139650.if3 | 139650bv2 | \([1, 0, 0, -95848313, 342101818617]\) | \(52974743974734147769/3152005008998400\) | \(5794222457869574400000000\) | \([2, 2]\) | \(30965760\) | \(3.5045\) | |
| 139650.if4 | 139650bv1 | \([1, 0, 0, 4503687, 22079290617]\) | \(5495662324535111/117739817533440\) | \(-216437059265495040000000\) | \([2]\) | \(15482880\) | \(3.1579\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.if have rank \(1\).
Complex multiplication
The elliptic curves in class 139650.if do not have complex multiplication.Modular form 139650.2.a.if
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
