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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 44100h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44100.bo4 | 44100h1 | \([0, 0, 0, -426300, -107058875]\) | \(10788913152/8575\) | \(6809671181250000\) | \([2]\) | \(331776\) | \(1.9684\) | \(\Gamma_0(N)\)-optimal |
| 44100.bo3 | 44100h2 | \([0, 0, 0, -518175, -57538250]\) | \(1210991472/588245\) | \(7474295088540000000\) | \([2]\) | \(663552\) | \(2.3150\) | |
| 44100.bo2 | 44100h3 | \([0, 0, 0, -1455300, 556817625]\) | \(588791808/109375\) | \(63319519019531250000\) | \([2]\) | \(995328\) | \(2.5177\) | |
| 44100.bo1 | 44100h4 | \([0, 0, 0, -22127175, 40060770750]\) | \(129348709488/6125\) | \(56734289041500000000\) | \([2]\) | \(1990656\) | \(2.8643\) |
Rank
sage: E.rank()
The elliptic curves in class 44100h have rank \(1\).
Complex multiplication
The elliptic curves in class 44100h do not have complex multiplication.Modular form 44100.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
