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SageMath
E = EllipticCurve("ij1")
E.isogeny_class()
Elliptic curves in class 73920ij
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.ii4 | 73920ij1 | \([0, 1, 0, -225, 9375]\) | \(-4826809/144375\) | \(-37847040000\) | \([2]\) | \(49152\) | \(0.71017\) | \(\Gamma_0(N)\)-optimal |
| 73920.ii3 | 73920ij2 | \([0, 1, 0, -8225, 282975]\) | \(234770924809/1334025\) | \(349706649600\) | \([2, 2]\) | \(98304\) | \(1.0567\) | |
| 73920.ii2 | 73920ij3 | \([0, 1, 0, -13025, -90465]\) | \(932288503609/527295615\) | \(138227381698560\) | \([2]\) | \(196608\) | \(1.4033\) | |
| 73920.ii1 | 73920ij4 | \([0, 1, 0, -131425, 18294815]\) | \(957681397954009/31185\) | \(8174960640\) | \([2]\) | \(196608\) | \(1.4033\) |
Rank
sage: E.rank()
The elliptic curves in class 73920ij have rank \(0\).
Complex multiplication
The elliptic curves in class 73920ij do not have complex multiplication.Modular form 73920.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
