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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 3675.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3675.h1 | 3675a2 | \([0, -1, 1, -251533, -48572532]\) | \(-19539165184/46875\) | \(-4222266357421875\) | \([]\) | \(24192\) | \(1.8776\) | |
| 3675.h2 | 3675a1 | \([0, -1, 1, 5717, -338157]\) | \(229376/675\) | \(-60800635546875\) | \([]\) | \(8064\) | \(1.3283\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3675.h have rank \(1\).
Complex multiplication
The elliptic curves in class 3675.h do not have complex multiplication.Modular form 3675.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
