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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 26775x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26775.n4 | 26775x1 | \([1, -1, 1, 3145, -114978]\) | \(302111711/669375\) | \(-7624599609375\) | \([2]\) | \(49152\) | \(1.1560\) | \(\Gamma_0(N)\)-optimal |
| 26775.n3 | 26775x2 | \([1, -1, 1, -24980, -1239978]\) | \(151334226289/28676025\) | \(326637847265625\) | \([2, 2]\) | \(98304\) | \(1.5026\) | |
| 26775.n2 | 26775x3 | \([1, -1, 1, -120605, 15016272]\) | \(17032120495489/1339001685\) | \(15252066068203125\) | \([2]\) | \(196608\) | \(1.8492\) | |
| 26775.n1 | 26775x4 | \([1, -1, 1, -379355, -89833728]\) | \(530044731605089/26309115\) | \(299677263046875\) | \([2]\) | \(196608\) | \(1.8492\) |
Rank
sage: E.rank()
The elliptic curves in class 26775x have rank \(0\).
Complex multiplication
The elliptic curves in class 26775x do not have complex multiplication.Modular form 26775.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
