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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 123840.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.di1 | 123840eu4 | \([0, 0, 0, -39468, 775312]\) | \(284630612552/153846045\) | \(3675054630666240\) | \([2]\) | \(589824\) | \(1.6777\) | |
| 123840.di2 | 123840eu2 | \([0, 0, 0, -23268, -1356608]\) | \(466566337216/3744225\) | \(11180195942400\) | \([2, 2]\) | \(294912\) | \(1.3311\) | |
| 123840.di3 | 123840eu1 | \([0, 0, 0, -23223, -1362152]\) | \(29687332481344/1935\) | \(90279360\) | \([2]\) | \(147456\) | \(0.98457\) | \(\Gamma_0(N)\)-optimal |
| 123840.di4 | 123840eu3 | \([0, 0, 0, -7788, -3133712]\) | \(-2186875592/176326875\) | \(-4212073820160000\) | \([2]\) | \(589824\) | \(1.6777\) |
Rank
sage: E.rank()
The elliptic curves in class 123840.di have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.di do not have complex multiplication.Modular form 123840.2.a.di
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.
