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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 83391.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83391.e1 | 83391l4 | \([1, 1, 1, -66956302, -66188478106]\) | \(705629104434579771433/368156220977687373\) | \(17320233761525983805360613\) | \([2]\) | \(14837760\) | \(3.5347\) | |
| 83391.e2 | 83391l2 | \([1, 1, 1, -37908437, 89066550746]\) | \(128058892751492323993/1238715547642881\) | \(58276464247256810023161\) | \([2, 2]\) | \(7418880\) | \(3.1881\) | |
| 83391.e3 | 83391l1 | \([1, 1, 1, -37819992, 89506334664]\) | \(127164651399625564873/12072019113\) | \(567938774619923553\) | \([4]\) | \(3709440\) | \(2.8415\) | \(\Gamma_0(N)\)-optimal |
| 83391.e4 | 83391l3 | \([1, 1, 1, -10275692, 216177177746]\) | \(-2550558824302680073/427664014254832509\) | \(-20119830322615153893345429\) | \([2]\) | \(14837760\) | \(3.5347\) |
Rank
sage: E.rank()
The elliptic curves in class 83391.e have rank \(0\).
Complex multiplication
The elliptic curves in class 83391.e do not have complex multiplication.Modular form 83391.2.a.e
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.
