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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 369600ec
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ec4 | 369600ec1 | \([0, -1, 0, -155233, -86033663]\) | \(-100999381393/723148272\) | \(-2962015322112000000\) | \([2]\) | \(4718592\) | \(2.2275\) | \(\Gamma_0(N)\)-optimal |
| 369600.ec3 | 369600ec2 | \([0, -1, 0, -4027233, -3102321663]\) | \(1763535241378513/4612311396\) | \(18892027478016000000\) | \([2, 2]\) | \(9437184\) | \(2.5741\) | |
| 369600.ec2 | 369600ec3 | \([0, -1, 0, -5611233, -433281663]\) | \(4770223741048753/2740574865798\) | \(11225394650308608000000\) | \([2]\) | \(18874368\) | \(2.9207\) | |
| 369600.ec1 | 369600ec4 | \([0, -1, 0, -64395233, -198875745663]\) | \(7209828390823479793/49509306\) | \(202790117376000000\) | \([2]\) | \(18874368\) | \(2.9207\) |
Rank
sage: E.rank()
The elliptic curves in class 369600ec have rank \(1\).
Complex multiplication
The elliptic curves in class 369600ec do not have complex multiplication.Modular form 369600.2.a.ec
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 Cremona 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 Cremona labels.
