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SageMath
E = EllipticCurve("ob1")
E.isogeny_class()
Elliptic curves in class 310464.ob
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.ob1 | 310464ob3 | \([0, 0, 0, -1242444, 533043952]\) | \(37736227588/33\) | \(185485360693248\) | \([2]\) | \(3538944\) | \(2.0382\) | |
| 310464.ob2 | 310464ob4 | \([0, 0, 0, -184044, -18763472]\) | \(122657188/43923\) | \(246881015082713088\) | \([2]\) | \(3538944\) | \(2.0382\) | |
| 310464.ob3 | 310464ob2 | \([0, 0, 0, -78204, 8204560]\) | \(37642192/1089\) | \(1530254225719296\) | \([2, 2]\) | \(1769472\) | \(1.6916\) | |
| 310464.ob4 | 310464ob1 | \([0, 0, 0, 1176, 425320]\) | \(2048/891\) | \(-78251636542464\) | \([2]\) | \(884736\) | \(1.3450\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.ob have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.ob do not have complex multiplication.Modular form 310464.2.a.ob
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.
