Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 385112.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 385112.l1 | 385112l4 | \([0, 0, 0, -23620379, -44185360858]\) | \(9614292367656708/2093\) | \(317275254453248\) | \([2]\) | \(8650752\) | \(2.6069\) | |
| 385112.l2 | 385112l3 | \([0, 0, 0, -1719779, -447331922]\) | \(3710860803108/1577224103\) | \(239089430773588548608\) | \([4]\) | \(8650752\) | \(2.6069\) | |
| 385112.l3 | 385112l2 | \([0, 0, 0, -1476439, -690233910]\) | \(9392111857872/4380649\) | \(166014276892662016\) | \([2, 2]\) | \(4325376\) | \(2.2604\) | |
| 385112.l4 | 385112l1 | \([0, 0, 0, -77234, -14417895]\) | \(-21511084032/25465531\) | \(-60317000327072944\) | \([2]\) | \(2162688\) | \(1.9138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 385112.l have rank \(2\).
Complex multiplication
The elliptic curves in class 385112.l do not have complex multiplication.Modular form 385112.2.a.l
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.
