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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 93600.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93600.h1 | 93600bx4 | \([0, 0, 0, -282675, 57838250]\) | \(428320044872/73125\) | \(426465000000000\) | \([2]\) | \(589824\) | \(1.8138\) | |
| 93600.h2 | 93600bx3 | \([0, 0, 0, -120675, -15588250]\) | \(33324076232/1285245\) | \(7495548840000000\) | \([2]\) | \(589824\) | \(1.8138\) | |
| 93600.h3 | 93600bx1 | \([0, 0, 0, -19425, 713000]\) | \(1111934656/342225\) | \(249482025000000\) | \([2, 2]\) | \(294912\) | \(1.4672\) | \(\Gamma_0(N)\)-optimal |
| 93600.h4 | 93600bx2 | \([0, 0, 0, 53700, 4808000]\) | \(367061696/426465\) | \(-19897151040000000\) | \([2]\) | \(589824\) | \(1.8138\) |
Rank
sage: E.rank()
The elliptic curves in class 93600.h have rank \(1\).
Complex multiplication
The elliptic curves in class 93600.h do not have complex multiplication.Modular form 93600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
