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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3822.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3822.t1 | 3822x3 | \([1, 1, 1, -20434, -1132783]\) | \(8020417344913/187278\) | \(22033069422\) | \([2]\) | \(9216\) | \(1.0969\) | |
| 3822.t2 | 3822x2 | \([1, 1, 1, -1324, -16759]\) | \(2181825073/298116\) | \(35073049284\) | \([2, 2]\) | \(4608\) | \(0.75035\) | |
| 3822.t3 | 3822x1 | \([1, 1, 1, -344, 2057]\) | \(38272753/4368\) | \(513890832\) | \([4]\) | \(2304\) | \(0.40378\) | \(\Gamma_0(N)\)-optimal |
| 3822.t4 | 3822x4 | \([1, 1, 1, 2106, -85359]\) | \(8780064047/32388174\) | \(-3810436282926\) | \([2]\) | \(9216\) | \(1.0969\) |
Rank
sage: E.rank()
The elliptic curves in class 3822.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3822.t do not have complex multiplication.Modular form 3822.2.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.
