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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 46410.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.t1 | 46410w4 | \([1, 0, 1, -114321714, 470469100036]\) | \(165237984118746893981597764249/573648406879275000000\) | \(573648406879275000000\) | \([2]\) | \(7962624\) | \(3.2028\) | |
| 46410.t2 | 46410w2 | \([1, 0, 1, -7246194, 7131909892]\) | \(42077845747243642058108569/2373576194711554560000\) | \(2373576194711554560000\) | \([2, 2]\) | \(3981312\) | \(2.8563\) | |
| 46410.t3 | 46410w1 | \([1, 0, 1, -1327474, -448786684]\) | \(258702909467786448334489/62746322151879475200\) | \(62746322151879475200\) | \([2]\) | \(1990656\) | \(2.5097\) | \(\Gamma_0(N)\)-optimal |
| 46410.t4 | 46410w3 | \([1, 0, 1, 5129806, 28982975492]\) | \(14928860414851539366915431/371514241287132224299200\) | \(-371514241287132224299200\) | \([2]\) | \(7962624\) | \(3.2028\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.t have rank \(1\).
Complex multiplication
The elliptic curves in class 46410.t do not have complex multiplication.Modular form 46410.2.a.t
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.
