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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 317400q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317400.q4 | 317400q1 | \([0, -1, 0, -52322508, 932437401012]\) | \(-26752376766544/618796614375\) | \(-366416427676773217500000000\) | \([2]\) | \(77856768\) | \(3.7779\) | \(\Gamma_0(N)\)-optimal |
| 317400.q3 | 317400q2 | \([0, -1, 0, -1787707008, 28965838614012]\) | \(266763091319403556/1355769140625\) | \(3211239840179006250000000000\) | \([2, 2]\) | \(155713536\) | \(4.1245\) | |
| 317400.q1 | 317400q3 | \([0, -1, 0, -28568332008, 1858564577364012]\) | \(544328872410114151778/14166950625\) | \(67110948166111380000000000\) | \([2]\) | \(311427072\) | \(4.4710\) | |
| 317400.q2 | 317400q4 | \([0, -1, 0, -2773234008, -6522988655988]\) | \(497927680189263938/284271240234375\) | \(1346635064487304687500000000000\) | \([2]\) | \(311427072\) | \(4.4710\) |
Rank
sage: E.rank()
The elliptic curves in class 317400q have rank \(0\).
Complex multiplication
The elliptic curves in class 317400q do not have complex multiplication.Modular form 317400.2.a.q
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.
