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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 59150h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.s3 | 59150h1 | \([1, -1, 0, -8450792, 8652791616]\) | \(884984855328729/83492864000\) | \(6296939177984000000000\) | \([2]\) | \(3870720\) | \(2.9210\) | \(\Gamma_0(N)\)-optimal |
| 59150.s2 | 59150h2 | \([1, -1, 0, -30082792, -53842056384]\) | \(39920686684059609/6492304000000\) | \(489642365280250000000000\) | \([2, 2]\) | \(7741440\) | \(3.2676\) | |
| 59150.s4 | 59150h3 | \([1, -1, 0, 54417208, -301849556384]\) | \(236293804275620391/658593925444000\) | \(-49670423229350440562500000\) | \([2]\) | \(15482880\) | \(3.6142\) | |
| 59150.s1 | 59150h4 | \([1, -1, 0, -460694792, -3805764412384]\) | \(143378317900125424089/4976562500000\) | \(375326822875976562500000\) | \([2]\) | \(15482880\) | \(3.6142\) |
Rank
sage: E.rank()
The elliptic curves in class 59150h have rank \(0\).
Complex multiplication
The elliptic curves in class 59150h do not have complex multiplication.Modular form 59150.2.a.h
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.
