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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 248430q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248430.q3 | 248430q1 | \([1, 1, 0, -247982998, 1502972780548]\) | \(2969894891179808929/22997520\) | \(13059584481197938320\) | \([2]\) | \(41287680\) | \(3.2601\) | \(\Gamma_0(N)\)-optimal |
| 248430.q2 | 248430q2 | \([1, 1, 0, -248148618, 1500864471072]\) | \(2975849362756797409/8263842596100\) | \(4692782114031862663640100\) | \([2, 2]\) | \(82575360\) | \(3.6067\) | |
| 248430.q4 | 248430q3 | \([1, 1, 0, -150184388, 2698006954518]\) | \(-659704930833045889/5156082432978750\) | \(-2927980674677382274147128750\) | \([2]\) | \(165150720\) | \(3.9532\) | |
| 248430.q1 | 248430q4 | \([1, 1, 0, -348762768, 168793493562]\) | \(8261629364934163009/4759323790524030\) | \(2702673641145817879537045230\) | \([2]\) | \(165150720\) | \(3.9532\) |
Rank
sage: E.rank()
The elliptic curves in class 248430q have rank \(0\).
Complex multiplication
The elliptic curves in class 248430q do not have complex multiplication.Modular form 248430.2.a.q
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.
