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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 331056.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 331056.ev1 | 331056ev1 | \([0, 0, 0, -476256, -147943312]\) | \(-2258403328/480491\) | \(-2541726662216822784\) | \([]\) | \(6220800\) | \(2.2530\) | \(\Gamma_0(N)\)-optimal |
| 331056.ev2 | 331056ev2 | \([0, 0, 0, 3357024, 855609392]\) | \(790939860992/517504691\) | \(-2737523639229409603584\) | \([]\) | \(18662400\) | \(2.8023\) |
Rank
sage: E.rank()
The elliptic curves in class 331056.ev have rank \(1\).
Complex multiplication
The elliptic curves in class 331056.ev do not have complex multiplication.Modular form 331056.2.a.ev
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
