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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 308112.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308112.h1 | 308112h3 | \([0, -1, 0, -4382184, 3532349808]\) | \(19312898130234073/84888\) | \(40906704125952\) | \([2]\) | \(5308416\) | \(2.2402\) | |
| 308112.h2 | 308112h2 | \([0, -1, 0, -274024, 55203184]\) | \(4722184089433/9884736\) | \(4763358435999744\) | \([2, 2]\) | \(2654208\) | \(1.8936\) | |
| 308112.h3 | 308112h4 | \([0, -1, 0, -179944, 93587824]\) | \(-1337180541913/7067998104\) | \(-3405999755007983616\) | \([2]\) | \(5308416\) | \(2.2402\) | |
| 308112.h4 | 308112h1 | \([0, -1, 0, -23144, 210288]\) | \(2845178713/1609728\) | \(775712315277312\) | \([2]\) | \(1327104\) | \(1.5470\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308112.h have rank \(0\).
Complex multiplication
The elliptic curves in class 308112.h do not have complex multiplication.Modular form 308112.2.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 LMFDB 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 LMFDB labels.
