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SageMath
E = EllipticCurve("ij1")
E.isogeny_class()
Elliptic curves in class 352800ij
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.ij3 | 352800ij1 | \([0, 0, 0, -9815925, 11464260500]\) | \(1219555693504/43758225\) | \(3752973220095225000000\) | \([2, 2]\) | \(14155776\) | \(2.9100\) | \(\Gamma_0(N)\)-optimal |
| 352800.ij1 | 352800ij2 | \([0, 0, 0, -155676675, 747623465750]\) | \(608119035935048/826875\) | \(567342890415000000000\) | \([2]\) | \(28311552\) | \(3.2565\) | |
| 352800.ij4 | 352800ij3 | \([0, 0, 0, 3689700, 40582388000]\) | \(1012048064/130203045\) | \(-714688647170460480000000\) | \([2]\) | \(28311552\) | \(3.2565\) | |
| 352800.ij2 | 352800ij4 | \([0, 0, 0, -24699675, -31564660750]\) | \(2428799546888/778248135\) | \(533978589715474680000000\) | \([2]\) | \(28311552\) | \(3.2565\) |
Rank
sage: E.rank()
The elliptic curves in class 352800ij have rank \(1\).
Complex multiplication
The elliptic curves in class 352800ij do not have complex multiplication.Modular form 352800.2.a.ij
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
