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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 54150.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54150.p1 | 54150bd4 | \([1, 0, 1, -11131827776, 452059378589198]\) | \(207530301091125281552569/805586668007040\) | \(592180226847589234410000000\) | \([2]\) | \(77414400\) | \(4.3503\) | |
| 54150.p2 | 54150bd3 | \([1, 0, 1, -2109715776, -28798258786802]\) | \(1412712966892699019449/330160465517040000\) | \(242698280806551051753750000000\) | \([2]\) | \(77414400\) | \(4.3503\) | |
| 54150.p3 | 54150bd2 | \([1, 0, 1, -706147776, 6841139869198]\) | \(52974743974734147769/3152005008998400\) | \(2317013321324103993600000000\) | \([2, 2]\) | \(38707200\) | \(4.0038\) | |
| 54150.p4 | 54150bd1 | \([1, 0, 1, 33180224, 441516701198]\) | \(5495662324535111/117739817533440\) | \(-86549585072498933760000000\) | \([2]\) | \(19353600\) | \(3.6572\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.p have rank \(1\).
Complex multiplication
The elliptic curves in class 54150.p do not have complex multiplication.Modular form 54150.2.a.p
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.
